How to engage the party when one player is significantly more social than the rest?

Question

My party has a warlock who IRL has high Charisma, and is fond of persuading, manipulating, and corrupting NPCs.

I am looking for ways to engage the rest of the players while not restricting the enjoyment of the warlock PC's player. I have noticed that the other PCs getting more distracted (checking phones, stacking dice, doodling, etc...) the longer they spend in town, or having a long discussion with an NPC. I would like to try to fix this.

Specifically, how do I keep the other players engaged and participating while the warlock PC attempts to persuade someone to join them/not fight them?

Answer 1

First, ask if it is really a problem. Are the rest of the players bored watching a one-man show, or are they amused and having fun watching this part?

If it really is a problem....

Call for a Roll

Shopping shouldn't take all session, and if the player has had a bit of the spotlight already that session, then there is no problem with saying,

DM: Alright, we need to move things along. You're trying to persuade the shop owner to give you a discount on what? What is the end result you're hoping for?

Warlock: The stakes, the wooden box and few bottles of potions.

DM: Great. Roll for persuation, with advantage.

**Warlock:**16.

DM: You talk at length and convice him to give you a 20 gp discount. Do you take it or leave it?

Don't always go this route, but sometimes you just have to move on.

While X, what are you doing?

Purposefully shift attention to the other players. It allows him to have his moment, but not loose

Warlock: Your stunning array of woodcraft is beautifully carved. How much would it take to buy one of these fine pieces?

DM: Okay, so the warlock is going to try sweet talk a deal with the shopkeeper. While he's doing that, what are you doing, Fighter?

You'll see Matt Mercer of Geek and Sundry's Critical Roll use this a lot when the party is shopping

NPC Shift Spotlight

Or even have the NPC make the shift.

Warlock: Your stunning array of woodcraft is beautifully carved. How much would it take...

DM[as NPC]: Yes, yes, sell your flattery elsewhere silver tounged worm. [to Dwarf] Do you hail from the kingdom under the mountain, Yes? So far from home. What dwarven work treasures do you have to trade?

Skill/Perception Interactions

Or if you have a player with high passive perception, pass that player a note while they're talking about something they notice, while the Warlock tries his thing.

You notice blood on the hem of the store keeper's tunic, and the shopkeeper is trying to hide it by holding his cloak close around him. As you watch him, something else seems off. Is his accent different than the last time you spoke with him? Where his eyes always that shade of gold? Something is just... off.

They can then choose what to do with the information. Maybe they let the warlock keep going to see what happens, but now they get to enjoy an aspect of it the Warlock doesn't know about. Maybe they will interrupt the Warlock, and try to get the party out of there. Maybe they will try to confront the shopkeep in the middle of the Warlock's corruption/manipulation/persuasion tactics. How fun for all involved if it played out like:

Warlock: Your stunning array of [DM slips not to Rogue] woodcraft is beautifully carved. How much would it take to buy one of these fine pieces? I'm sure I could pay a fair price of...

Rogue: I stab the shopkeeper while he's distracted.

DM: Roll for attack.

Warlock: Wait! What?

Answer 2

This answer is in support of J. A. Streich's answer, and hopefully adds experience/context on how this plays out.

I have this exact problem (coincidentally also a warlock). I'm playing two different groups with the same members (minus the DM of the first group). In both campaigns this player role-plays at the expense of the rest of the group.

In the first group I am a player and lack the agency required to do anything without actively disrupting him, although another player has essentially taken that route. The DM just lets him go non-stop. I believe one session recently I spent an hour and a half just listening to him explore the castle with his spider familiar.

I am the DM of the second group, and the same player continues this basic behaviour. However I now treat world exploration via pseudo-rounds. Every time somebody interacts with something, I ask what the other players are doing, and if they want to do something that competes with one another, rolls dictate the result.

This has resulted in significantly increased player immersion, and often amusing incidents that simply don't happen in the other group.