Most tabletop RPG games are set up that you are a cohesive group, a party of extraordinary people who, for the most part anyway, works towards a common and worthwhile goal. While the game pits you against monster, villains, and even rival groups perhaps, they are rarely ever set up so that you can throw down against your friends and one time allies. Generally, this is because fighting against your friends could breed contempt among the real life people playing the game, and no one wants their friendship to end because someone’s mage sent a lightning bolt. But does it have to be this way? Is there no way to have a player versus player, or PVP section in your game without there being bad feelings? I think there is.
Firstly, everyone needs to know that’s what’s going on, and be into it. As in all things, consent is super important, and only when everyone knows what something is going be can they agree to it. This, of course, includes the stakes involved. Are the fights to the death, or non-lethal? If someone does die, is there a way to resurrect them, or are these characters even things you care about enough to bother with such abilities? All of these things and more should be figured it long before anyone sits down to play.
Once you've gotten all that out, make sure the PVP is fun. Make interesting terrain features, cool magical area effects, or intersperse the inter-player combat with moments where they'd face to come together to fight of something that's too big for either to face alone.
PVP could be something fun for your players to enjoy should you feel like including it and follow these simple instructions. Sometimes it can provide a kind of cathartic release that could be good for a group, both in character and outside of it.