Setup: Combat has been going on for three rounds. Goblins (Initiative 19) vs. Players.  The battle seems to be swinging towards the players so the Goblins Disengage to the next area where more Goblins are waiting to ambush the party.  

Question: Focusing on Initiative.  Would the new Goblins in the other area, once meet up with the fleeing Goblins and introduced into combat, take on the original Goblins Initiative order since the two groups merged as one or would that group need to make their own roll and placement?

This is definitely one of those, "Whatever the DM finds easiest" questions. If we're going hard by-the-rules, each individual creature would get its own initiative. Personally I don't like giving all the creatures a single initiative, because it makes it too easy for them to bum-rush opponents, so in a situation where there's too many creatures to be worth the effort of tracking them all individually I would still roll separate initiative for the new group of goblins. I think the main reason to just add them to the same initiative order would be if you don't have an easy way to tell one group from the other.

Quote from TransmorpherDDS >>

This is definitely one of those, "Whatever the DM finds easiest" questions. If we're going hard by-the-rules, each individual creature would get its own initiative. Personally I don't like giving all the creatures a single initiative, because it makes it too easy for them to bum-rush opponents, so in a situation where there's too many creatures to be worth the effort of tracking them all individually I would still roll separate initiative for the new group of goblins. I think the main reason to just add them to the same initiative order would be if you don't have an easy way to tell one group from the other.

I would not want to do individual roll per-monster that seems like more work than necessary and a combat killer ("Please hold on while I roll individual initiative for these 10 kobolds.  Oops, we have a roll-off.  ") I did not find anything in DMG or PHB I wanted to be sure if there was a rule that I had overlooked and I prefer trying to find the rules before 'adjusting'.  Since I'm running on a VTT marking different groups would be pretty simple to distinguish one group from another so it is possible to define them under separate initiative rolls.  

Yeah, I would personally do them as different groups of goblins too. But, like TransmorpherDDS stated, it’s up to the DM whatever they find easiest to do.

Having the "Goblin Group B" goblins all enter on a set initiative count (20 or 0, probably) is how I'd normally run it. The MM already encourages the use of static initiative marker 20 for lair actions, and introducing a second wave of combatants midway through a combat seems analogous to the encounter popping its lair action. 

I use encounter managers tools to roll initiative for all monsters and sort them automatically, so I'd just add them to the turn order with that.

But as others have mentioned, it is up to DM preference. I personally hate having all my monsters moving on the same initiative, it makes the game feel even more turn based (enemy phase - player phase - enemy phase).

Quote from DxJxC >>

I use encounter managers tools to roll initiative for all monsters and sort them automatically, so I'd just add them to the turn order with that.

But as others have mentioned, it is up to DM preference. I personally hate having all my monsters moving on the same initiative, it makes the game feel even more turn based (enemy phase - player phase - enemy phase).

 Do you use DDB Combat Encounter Tool or some other utility?

Last time I used it DDB encounter didn’t sort...

Even in an encounter with just goblins I'd have them in a few squads that use different tactics - like a skirmishing group and a ranged group each with their own initiative. In this case it seems like it might be appropriate for the skirmishing group to lure the party into a room set up to benefit the ranged group.

Quote from TransmorpherDDS >>

This is definitely one of those, "Whatever the DM finds easiest" questions. If we're going hard by-the-rules, each individual creature would get its own initiative. Personally I don't like giving all the creatures a single initiative, because it makes it too easy for them to bum-rush opponents, so in a situation where there's too many creatures to be worth the effort of tracking them all individually I would still roll separate initiative for the new group of goblins. I think the main reason to just add them to the same initiative order would be if you don't have an easy way to tell one group from the other.

 I definitely think it's more fair when each monster has their own Initiative just like each player does, but it does make more work for the DM, especially when you're dealing with creatures like goblins or kobolds that often appear in packs. VTT's can definitely help in that regard, one of the platforms I play on is especially good at that. I wouldn't want to track a 6-player party and a horde of goblins on paper :(

I usually give each monster type its own initiative. It's rare that I'd design an encounter with only goblins. There might be a shaman, or some wolves or something else in it to force the players to mix up tactics, and to make things more interesting for me when I'm running it. Then I'd give the goblins one initiative roll, the wolves one and the shaman one. It kind of splits the difference between each creature, and the whole side at once.

But to answer the OP question. I'd probably do, as others have said, a second group of goblins on its own initiative. Though as I'm typing it, I realize that could get messy trying to remember which one was in which group, so maybe not.

Quote from BKThomson >>

Quote from DxJxC >>

I use encounter managers tools to roll initiative for all monsters and sort them automatically, so I'd just add them to the turn order with that.

But as others have mentioned, it is up to DM preference. I personally hate having all my monsters moving on the same initiative, it makes the game feel even more turn based (enemy phase - player phase - enemy phase).

 Do you use DDB Combat Encounter Tool or some other utility?

 I used to use toolbox extension (I forget exact name). But used DDB combat tracker last time.

Quote from Chicken_Champ >>

Last time I used it DDB encounter didn’t sort...

 It does now. There is even a button for "auto roll monster initiative."

Ah, I'd seen the "auto roll initiative" button, but I'd either missed the "start" button that then actually sorts them following that roll, or it's new. 

I group all monsters that are the same (in terms of name/statblock), and if more enter the fray of the same type I keep them on the same initiative.

Now, if I have 2 goblin "rogues" and a goblin "sentinel" enters the fray, that's a different statblock/creature type, so it gets its own initiative.

But if it's just regular gobbos and more gobbos arrive, they keep the gobbo initiative order.

I wish I could track every individual initiative. But I'm old and have a hard enough time tracking everything else that goes on in a fight.