I beg you: do not give your VtM setting a Prince.
If you're running a standard Camarilla game, or, especially, a political intrigue game, try deliberately not creating a central figure of authority who can simply arbitrate disputes and declare what is and isn't permissible. It very easily, even unintentionally, turns into GMPCism.
You have this extremely powerful NPC sitting at the top of the political hierarchy, and whenever the players do something interesting, the Prince can effectively go "No." Suddenly this character becomes the GM's veto button. The coterie can scheme, investigate, negotiate, threaten, betray, and maneuver all they want, but ultimately there is some 300-year-old vampire in a mansion whose opinion supersedes everything they've done.
Instead, make the political order unstable. Take away the obvious final arbiter and let the players discover what actually happens when nobody has the authority to settle things.
Maybe a Sabbat raid killed half the city's elders three months ago. The surviving Kindred are desperately trying to reconstruct a functioning hierarchy, but nobody has enough legitimacy to claim the throne.
Maybe the Prince disappeared, and the Primogen are now fighting over whether the position should even be restored.
Maybe the city is a newly established domain where a handful of Anarchs have carved out territory and everyone is still pretending there are rules.
Maybe the old Prince technically still exists, but has become so weak, isolated, or politically irrelevant that everyone has quietly stopped obeying them.
Maybe there are competing claimants to Praxis, and the coterie's actions can genuinely determine which one wins.
Or don't even make the city a coherent political unit. Give the characters a dozen overlapping power structures: a Ventrue banking family that controls mortal finance, a Brujah neighborhood militia, a Nosferatu information network, an old Tremere chantry that refuses to recognize the city's new government, and three Anarch barons who all insist that their territory is independent.
Now suddenly everything matters. If the coterie pisses off the Ventrue, there isn't a Prince they can appeal to. If they kill someone important, there isn't necessarily an elder who can simply declare the matter closed. If they make an alliance, that alliance can actually change the balance of power. If they convince two factions to cooperate, they have accomplished something that might genuinely reshape the city.
Most importantly, the players become political actors rather than petitioners.
VtM is at its most interesting when authority is something characters have to negotiate, manufacture, contest, and sometimes violently enforce, not an NPC sitting in a tower who exists to tell everyone what the rules are.
Take away the Prince. Watch the consequences become 200% more consequential.