Just finished a combat where I cast Hex but then managed to de-escalate the combat and have it resolve peacefully. Everyone went their own separate ways and my Hex target walked away without ever being reduced to 0 hit points. What happens to my Hex after that? Does it remain on the non-hostile target or can I move it to a hostile target during my next encounter?
All you can do is drop concentration and let the spell die, or maintain concentration and leave it on that creature. The spell, I'm afraid, is effectively wasted.
The wording for Hex states:
If the target drops to 0 hit points before the spell ends, you can use a bonus action on a subsequent turn of yours to curse a new creature
That is the only condition on which you can move the spell to a new target, so unless someone else ends the current target for you (or you change your mind and do it yourself), you are out of luck.
BUT! If you can wait an hour before your next combat, you'll regain that spell slot (assuming conditions are good for a short rest), so no net harm done! Assuming you are a Warlock, of course...
If the target drops to 0 hit points before this spell ends, you can use a bonus action on a turn of yours to curse a new creature.
If your target doesn't drop to 0, you can't choose a new one. You can still maintain the spell on that target for as long as your concentration allows, even if combat between you ends.