When I started DMing a couple of months ago, it was with a group of people whom I know very well.  We had a session zero, but it was short and sweet because everybody already knew what everybody wanted, and everything was compatible.  This week, a new player will be joining us, someone who is well-known to one of my players, but whom I have never met.  I have already established a conversation with him via Discord, with a short explanation of the existing rules and preferences.  I know he intends to be a human fighter/monk with the acolyte background, but not much else; it has been extremely difficult getting him to talk to me.  I think it’s shyness and/or introversion, based on my observations and the other player’s description of him

The tone of the game and personal boundaries have already been well-established amongst the original group.  I’m not sure if a second session zero would be helpful or unnecessary.  My biggest priority is that my table be a safe, fun environment for everyone involved (I have had some very bad experiences with toxic D&D groups).  A whole session seems a bit much, since everybody has their characters and basic preferences down, but I also don’t want to just drop him into the group with no ado whatsoever.  Does anyone have any ideas?  Have you ever had a similar experience?  Are there any specific questions I should ask or say?  Any advice and perspectives are greatly appreciated!

I wouldn't spend a whole session on introducing a new player, but I think pause to break the ice between the new player and most of the table in a session 0 style would be worthwhile.  An "around the (virtual?) table" where everyone gives a hello and probably a couple of sentences about their character.  DM goes over any house rules and 'social contract' stuff (might be to DMs benefit to do the house rules and delegate whatever social contract stuff exists at your table to the players, that way you demonstrate it's something important to the whole table).  Lastly _integrate_ the back story.  Your game's PCs are already bonded, I'd recommended this new character and an existing character (like the player most familiar with them) have some sort of backstory bond, doesn't have to be elaborate ... maybe as broad as having fought in the same side in a war or as trivial as both having seen their families duped by the hometown swindle, leaving them adventure as their only route to seek fortune."  That way you already have some integration storywise to get the character more involved in the game.

Fostering a safe environment starts with a Session Zero where everyone gets to know each other and share in setting the boundaries of the game. But it is also a continual process that should be woven into the game during every play session. There's a really great video on youtube that explains this in incredible detail - 

https://www.youtube.com/watch?v=g-mjkcjWaZ0

I found it very eye opening.

I've been in your position. Started a game and one of my players brother wanted to join. I said ok and wrote up a story line that led him into the others. You don't need a second session zero. Just have a one on one before the game kicks off. That's what I did and he stayed in the game with the others for over a year. 

You'll be fine. 

Personally I don’t have a specific session zero but, I do have a private one on one with the player, either arrange to jump online a day or 2 before, just to talk through character sheet, background, if the campaign is a bit more mature agree how much cash they are starting off with and what they may have been able to buy magic item wise already. 

I then don’t just drop them into the campaign? I will find the right story beat moment to introduce them, maybe they are held captive in the dungeon the party are in, maybe they have a link to the enemy the players are hunting down. I will then have them dial into the game, but explain that they will be introduced when the moment is right and based on what the players do. Once that was almost 2 sessions as the other characters where drawn into a side quest a little longer then I anticipated. But the player actually said that was useful because they could watch the other players, see how I DM, and get a feel for the style of the table without just jumping in with a character. There is also the expectation as every new NPC is met with the players wondering, is this the new character, waiting for me to turn to the player and say. “Describe what you look like please” in that situation it was one of the last things that happened and so session 3 start the proper introductions happened. 

Quote from AnzioFaro >>

Fostering a safe environment starts with a Session Zero where everyone gets to know each other and share in setting the boundaries of the game. But it is also a continual process that should be woven into the game during every play session. There's a really great video on youtube that explains this in incredible detail - 

https://www.youtube.com/watch?v=g-mjkcjWaZ0

I found it very eye opening.

I was "meh" about consent rules in D&D when I first heard it was a thing.  My initial reaction was "HR in D&D too?"  However, understanding the thinking behind it gave me a greater consideration at my tables.  I always thought of myself as a considerate DM, but some viewing and reading and talking with other players identified some blind spots for me too.  Aside from educating via YouTubers, Monte Cooke games' publishes a free resource, which includes the philosophy behind consent and boundary rules in TTRPG, as well as some tools, including a pretty handy form, it actually makes boundary discussions pretty quick and efficient (the last thing you want to do in a boundary discussion is belabor the boundary discussion, because you are in that case de facto pushing or questioning boundaries):

https://www.montecookgames.com/consent-in-gaming/

I sense though that the OP is pretty sensitive about these matters, so I guess this post is more for other readers of this thread. 

I had something like this happen... one of my players had a friend who wanted to join. I did a separate session 0 with the new player and the existing player who was her friend. The rest of the group was not involved. This allowed me to get to know the new player, ask her questions, basically do the session 0 with her. The existing player was there to make introductions, help answer questions and so forth. That went well... then I did a separate character creation session with just me and the new player. That also went well, so we added her to the group. We have not had any issues.

I did get agreement from all the other players to add her before even having the 2 sessions with her. I also figured my existing player who was her friend, knew the type of person we were looking for and would not, at least knowingly, add a problematic person to the group. We did some introductions in the first session when she joined us, and the just added her to the play fairly quickly (she happened to be in a tavern when they came in to get some food, cliche' I know but I wanted to quickly get her involved). She also had booked passage on the one ship that was going the same way the players wanted to go (funny how that works out). So they all traveled together, all got caught by pirates together, etc.

We have not had any problems either before or after adding the new player.