dnd 5e – Does the Hunter’s Mark spell chain to multiple creatures?

First, this is a concentration spell, if your concentration breaks (p.203 PHB) the spell ends. It is also time limited – you can concentrate for up to 1 hour (1st or 2nd level slot), 8 hours (3rd or 4th level slot) or 24 hours (5th+ level slot).

Second, it does exactly what it says:

If the target drops to 0 hit
points before this spell ends, you can use a bonus action
on a subsequent turn of yours to mark a new creature.

So if a creature drops to 0 hit points and you keep concentrating then on a subsequent turn of yours (which can be in a completely different encounter 45 minutes later) you can use your bonus action to mark a new creature. And so on and so forth until the end of the spell.