Just tell everyone up front
I usually start PVP-games, or, really, any game, with a pre-character-creation talk about what is and isn't okay in the game, how I'm resolving the major rules contradictions and underspecifications that are applicable to most every character, and what players should expect from the game. In a game where I wanted to do this, I would say something like:
Not all the information I tell you will be true; it will be based on what I think your character should know given whatever skill and/or attribute checks you are using and your prior actions. For example, I might tell you that the inkeeper of the Red Flagon is a jovial middle aged man, when actually that's the innkeeper's assistant. I also might draw attention to useless or harmful information, or describe important characters in a way that makes them blend into the background, in accordance with NPC attempts at deception or being beneath notice
Similarly, not all the information you tell each other needs to be true. You can feel free to make characters that do not portray themselves honestly, and even to work at odds to the party if you feel like. Be aware that other players don't have to believe your lies or other deceptions, and will likely kill you and take your stuff if you, for example, play a Chaotic Neutral Changeling Rogue and treat them like blind idiots. It's expected that you keep information you are keeping secret from other player's characters also secret from said players, and that attribute checks, attack rolls, and saving throws will be used to resolve conflicts between player characters' attempts to do things, just like they are used to resolve those conflicts between PCs and NPCs.
As the GM, it's my responsibility to remain a largely impartial party in this game. You can't misinform me about your characters' actions or motives or whatever else, because I dictate how those things play out in the world and my being misinformed will just make your character ludonarrative actualization dissonant with your expectations. Because of this, it is generally a good idea to let me know, discreetly of course, what you are planning ahead of time if you are planning anything particularly crazy. I won't tell anybody else, at least until the campaign is most definitely over-- it's my responsibility to keep your secret plans secret out-of-character as well as yours.
If you need to tell me something discreetly, you can (insert system you are implementing for this here). This sort of game usually ends up with PCs getting attached to non-player characters with irreconcilable philosophical conflicts and then fighting each other as a double-sided metaphor with their character conflicts mirrored in the larger societal conflicts even as those societal conflicts are mirrored in the relational conflict. Hopefully everyone is ready for that. Any questions?
Normally in PvP games I GM sandbox-style. That means that, while I might suggest to a PC building a Wizard they might like to be a secret agent for a necromantic cult and join in with a party I had already going to stop said cult, I wouldn't expect them to say yes or to stick with that plan when it looked like the Paladin (or whoever) was catching on. I also wouldn't expect the party to stick with the mission based just on being hired by a noble, especially if they got payment in advance and were newer players. If I cared about the plot you are describing actually happening, I'd have to get player buy-in on being a party, and I'd have to do that while also allowing for party-breaking murder scenes and free-for-all combats and all of that. That would be hard, and I'd probably come up with some MacGuffin excuse why everyone needs to be here now, and why leaving isn't a realistic option for anyone at the start of the campaign.
I have also run this exact scenario emergently in a PvP game without the aforementioned requirements.
- The neophyte necromancer rapidly decided the party was the best thing
since sliced bread, what with the supply of corpses, not asking any
questions about the necromancy, lack of backstabbing for his
spellbook, full share of the loot, and rapid EXP gain. In the final
confrontation of the dungeon, when the master necromancer went to do
the big reveal he cast counterspell, smugly said "I really have no
idea what you are talking about", and then cast fireball (he had
levelled from 1-5 over the course of the dungeon). Then the fighter
beat the master necromancer to death with a greatsword+extra
attack+action surge, the rogue intimidated the remaining
newly-uncontrolled undead (not part of the contract), and they left
with the loot and never talked about it again.
What I'm saying is that intraparty PvP in PvP games doesn't normally happen with experienced players except for ideological reasons. The dude who's trying to murder the party is just being stupid if he's doing it for money or magic; there is almost no more dangerous opponent than an adventuring party of your peers. It's just safer to go pick a fight with a dragon instead.
With inexperienced players, it's totally different, of course.