Should a character meet an untimely death and the player creates a new character to continue with, what is a good way to introduce them to the party? What might be a good incentive to entice them to join and have the party accept them in character? Also, if a TPK occurs mid-campaign, how do you deal with that? I've played in games where the characters were captured instead of killed, but what other options are there? Do I restart the entire campaign and have the players make new characters? Do I have them make new characters of the same level (going by milestone) and find a way to shoehorn them to where the previous characters left off? What could be a good way to do that? Are there other options I haven't thought of?

Well perhaps when a player is killed or dies, try making the new character tied into the main conflict, giving the character a reason to stick with the party. Ex: "After the battle (where the old player died) the corpses of enemy soldiers and allies are laid bare. In the distance, you can see a young soldier bearing your banner mourn the loss of his friends before attempting to join you, vowing to avenge his friends." Ofc I did just make this up and I have no idea what your campaign is like so the situation may call for something else entirely but I hope you get the main gist of it. If it is a tpk, you can try setting the new party a couple months ahead in game time to where the conflict is bound to be much bigger than their first go, giving them roughly the same level they had from before and try and continue on from there. Either way, ur the dm and what you say goes, idk your game style or how long the campaign was supposed to be going but these are just my ideas. Hope this helps.

For adding a new character, we tend to try not to make a big deal of it. Here's this new person, the player describes what they are doing here. RP it for a couple minutes and then off we go. We'd rather get on with the main story than go through some exercise of someone deciding they don't trust the new person and needing to be convinced before we can carry on. I'm not saying that's a bad way to play, some groups really like that kind of character interaction. Just, in my group, we tend not to dwell on it much. As far as how to incorporate them. There's the classic, here's a prisoner you free, or someone's sibling coming to check on them. It can also be easy if you have a patron, or work for an organization, and just have that patron assign a new member to the group.

As far as a tpk. My favorite way is to say, well, now the bad guy won. Everyone roll up a new party while I figure out the repercussions and tell you what's changed in the world now that the cult has succeeded in raising the ancient evil. That really only works for homebrew, however. If I were running a published adventure. I'd probably just pick up where the old party left off. Yeah, it's a little cheesy, but folks usually don't want to re-play the first part of the same adventure.

First, I'd ask the player how they want to handle it. Some of them just want to kill off their current characters and start fresh without any special notice. Others want nice send-offs, or heroic goodbyes, or specific ties to some existing element of the campaign when they re-enter. Brainstorm with them when you can. Players have great ideas. 

I would recommend having the new character be at the same level as everyone else. It's easier to balance things that way and it doesn't lead to any feelings of unfairness. As for where to introduce them, it can be awkward in sealed dungeons, but it's still doable. At some level, everyone realizes it's just a game and players need to be integrated. 

Regarding TPKs, that's a conversation for your players. When my friends and I TPK'd toward the end of Tomb of Annihilation, we decided we preferred just to end the campaign there and start a new one. When we were on the verge of a TPK in the next campaign, we all agreed that we'd prefer to keep going - either rolling new characters or having an afterlife arc. (We ended up only losing half of our party, who rolled new characters and joined the survivors.) There's no right answer besides talking it out and seeing what everyone wants to do.

If you do have a death, however, know that it might be pretty emotional for some players. Communication is going to be important - in general as a DM, and in particular with how to move forward with major party changes. 

Whenever I have played and a new character needed to be introduced, they were normally held captive by the enemy we happened to be hunting down or had come across. We rescued them and they just so happened to be heading in the same direction as us and normally had some other reason for staying with us. In a dungeon crawl, you could find them tied up in a corner guarded by a couple guards. I am story oriented however and get slightly annoyed when we meet a character in the next tavern and they join us just because they feel like it. I think that the new character should have a reason they want to join the party other than the fact that they are there in the first place to play with the party. Maybe they are hunting down the same enemy, maybe they want the pay, maybe they are hiding from the police and going on a trek out in the middle of the wilderness would get them away from the law. It isn't really hard to come up with a reason, as long as there is a one.

As for a TPK, I have never been in one and have no idea how to handle it.  

We've had a couple characters die or be captured, or some such and had to bring in replacements, or in some cases, "temp" characters.  Our first, my daughter created a cleric who followed the Goddess my monk was following after having awakened her (my son's homebrew world)    Another, our fighter made a Cleric whose path paralleled our own for a time, after his character was killed and stuffed in a bag of holding for a later rez.  Currently, my daughter's boyfriend is playing a pal-lock whose patron sent him to the hells to wreak havok in his/her name (we still don't know anything about his patron) That character met us as we entered the hells, to retrieve his main character, our barbarian.

TPK is a group discussion.  If the group has/had a significant patron, that patron may have sings posted, or recruiters hunting for people to pick up the task.  Perhaps one or more of the original party is sent back by their God or Goddess, their work undone?  Whatever the group decides, there's usually a way that makes enough sense to allow you o pick up and carry on (ish, as I would ensure some connections the old party had were never made for the new ones)    If you are keeping good notes as DM, you may have fun times where they think a town is indebted to them, but it owed the OLD party a debt, not the new one..

I just realized that I had the perfect opportunity to talk about Death, something that I enjoy a lot, so I will be posting here again. 

A TPK might be the best time to introduce Death. Death could make a deal with them, allowing them to return to life as long as they held up their end of a bargain which could be something like slaying an undead creature, returning a lost soul, guiding another dead spirit to the afterlife, rescuing a creature that has passed on from fiends, causing or stopping an event that will end in many deaths, or giving a cat its ninth life. To make it more interesting, their return to life is temporary and while they are completing Deaths task, they are also attempting to find a way to stay in the mortal realm. 

For Death, I highly recommend Death from Discworld because he's just plain awesome, though having Death's apprentice (Mort) come would be equally cool. Maybe Death's apprentice is on his first job and it just so happens to be for the players. Something goes wrong, and they continue to live, but the cost of dying is even higher and maybe they see the Skeletal figure of death looming out of the shadows. Other harbingers of death could be Xolotl, the Aztec death god, Morrigan from Celtic mythology, Valkyries, The Grim Reaper, The Grim Weeper, (Grim Reaper's younger brother who he thinks of as a crybaby)who mourns the passing of all life with their eternal tears, or even better, the Grim Sweeper, who carries a broom and is surrounded by billowing clouds of graveyard dust, or maybe a something completely unexpected, like a black and white cowboy or the easter bunny. (Something that would cause the players to go, "Wait, you are the one that runs this whole life and death thing?") 

If you want, make up your own Death. Just research psychopomps, and choose which themes of mortality you want to use, like ravens, bones, vultures, dogs, and deer. It can be cool to have a tool that they use to execute their tasks, like a royal sword, a scythe, a sickle, or a broom. Since cats have nine lives (widely known fact) the cat lord or some other cat being would work well.

If the party has had interactions with other powerful beings of legend, maybe the party finds that that powerful fey lord or fiend that they bargained with a while ago is claiming their souls as their own. (Always read the fine print) You could even set this up in case you ever actually kill the whole party. Have the party meet some creatures like Baba Yaga, and they have to bargain with them or make a deal of some sort. Make the deal very hard to understand and cryptic, but may the benefits seem almost too good to be true. Then, when you accidentally TPK the players, you have a back up plan that could be a cool story point that surprises but makes sense to the players. 

New PC: I try to weave them into the story reasonably organically. It could be someone passing by, someone they meet on the road, it could even be an NPC that you flesh out and beef up who decides that they're willing to help in a more hands-on way.

TPK: Not too many good options here, honestly. Start again or roll up a new band of heroes who heard about the last group failing and turned up to try their luck. Ask your group what they would prefer. I mean, if they want to keep their existing PC's, there's always THE GODS. It's a fantasy game after all.

  One of the best ways Is to asked the players  how they  want to introduce  their characters and if it's reasonable  do it .Some of the best interactions at the table  and most amusing have come about this way. 

Quote from rammsorrow >>

  One of the best ways Is to asked the players  how they  want to introduce  their characters and if it's reasonable  do it .Some of the best interactions at the table  and most amusing have come about this way. 

This is true.  About four months ago, we lost a PC.  About three months before that, one of them turned out to have a long lost child, that they had never met, from a carousing event that was part of the player's backstory.

The player created that long lost kid, looking for the parent,. Totally motivated by the sessions, and all I had to do was say "sure".

The face on the Player when it turns out the other person was their kid was a trip -- and the kicker was that they were a mother and son pair, and yes, the mother became the child.

I used the standard "you come across a traveler on the road, cleaning up after a fight" line of entry.

My bard was once introduced thusly:

The players hear a distant scream. Looking around, it's a few moments for them to realise it's from above. They look up.

Someone is falling out of the sky. A continuous, panicked scream of 'AAAAaaaahhhhh....!!!' - while at the same time seeming to be frantically digging in a backpack.

The someone seems to find whatever he's looking for, holding it up triumphantly - a sheet of paper, that's almost instantly very nearly torn from his hands. 

Still screamning 'AAAAaaaahhhhh....!!!' he tries to read this paper. He is now dangerously close to the ground. The paper is blown violently by the wind. He calms his nerves, stops screaming, straightens the paper, and at the very last moment casts Feather Fall from the scroll. 

He lands gently, elegantly. Straightens his clothes and puts on a fancy hat.

'Well met, good travellers - I'm Clavius Windermere, bard, raconteur, poet, singer of songs and teller of tales. Allow me to inform you of my day thus far ...'

I had a player that didn't die but he had real life priorities (specifically Sunday football). So when he came back not only had 16 sessions-ish and 2 levels had passed with the party but the party was also entering combat. Also he had only played 2 previous sessions with the party and apparently wanted to change his name (in a way he was a new character). Should point out to that this is the entire group's first time playing dnd and really only second time playing a tabletop game. So I didn't want to leave a beginner player out. The insane way I made his character comeback was based on his and another character's subclass.

The character in question was playing a Fey Wanderer Ranger so during this time he was missing he was whisked away to the Feywild. While there he traded his memories and name for a powerful weapon. So he could keep up with the party and explain why his name was different. Also, lets me come up with some personal story stuff for him. How he got back to the party was with the other party member a Wild Magic Sorcerer. Her wild magic surge pulled him back from the Feywild.

Simple ways introducing replacement characters:

- Locked up prisoner

- Wanderer in distress

- Surprise ally in combat

- Sent by ally "I was looking for you, XYZ thought you might need some help"

- Knight errant "I've heard of your deeds, have my Sword/Axe/Bow!"

- The new character always has been in the party, but somehow, no one noticed. ;)

Stole this idea from XP to Level 3 and it's worked amazingly so far. I've changed it a bit to suit my needs:

There's a character called The Keeper. Whenever a player is unable to make it to a session, The Keeper will appear in-game. He will come out of a door that suddenly appears and will take the missing player with him. His job is to prevent paradoxes from occurring and also to prevent the entire multiverse from starting a war. When a character dies, have them meet The Keeper in "heaven". He will bring them back to life on a certain condition (whether that be a trade or a favour or something else).

As for new players being introduced, here are some options:

• The new player falls out of a portal in the sky. They land in a tree or a pond so they don't take damage.
• The new player runs straight into the party and falls over. Their character was running away from something.
• A prison cell in the middle of nowhere. For some reason, it's not guarded. The prisoner is the new player.

For continuing a game when a TPK has happened, I believe that I have found the ideal solution.

My players decided to make a base of operations, and this was the seed I needed - they wanted to make a school. So, they found the place, decided to advertise before the architects guild had even looked at repairing the building, and I asked them all to make their backup characters. The session ended with their backup characters all walking into the inn where the normal characters were, to apply for teaching positions in the school.

Now I have their backup characters already in the story, and ready to go should a TPK happen. They will receive word of the schools founders being lost, and they may well embark on a mission - plausibly to bring back their corpses and perform a resurrection ritual, so that the campaign can return (with consequences, of course!), should the players want to.

for introducing a new character, make sure that the players know that shunning a new character (or worse, becoming hostile) is not acceptable - some people spend hours making their characters, so players need to find good reasons for the group to get on with them and get to adventuring again!