Several features, like a Level 15 Battle Master's "Relentless", give one or more bonuses (in this case, a superiority die if you have none left) at the initiative roll of an encounter.
My question is : if a character leaves an (unresolved) encounter, then later comes back into the same (still unresolved) encounter, can he roll a new initiative (thus potentially getting initiative bonuses like the Relentless superiority die) or must he keep the previous one he had ?
This assumes the character would "act out of a turn" (ex: wait for about 20 seconds then jump back in), as he removed himself from the encounter, and thus from the initiative order.