My opponent has a unit at a battlefield with a hourglass in base. If I walk in (as attacker) and beat that unit in combat and trigger hourglass, can they replay Rengar Trophy Hunter to the same battlefield to start another combat? If so, are they the attacker or defender in this combat?

Yes — they can play Rengar to that battlefield after the first combat ends. And when they do, they are the Attacker in the new combat.

Here's the full sequence and why:

1. First combat: Ask moves in → applies Contested → is Attacker. Combat resolves, damage is dealt to the opponent's unit. Before it would die, Zhonya's Hourglass's replacement effect kicks in — the Hourglass is killed instead, and the opponent's unit is healed, exhausted, and recalled to base. Ask's unit remains alone at the battlefield.

2. Combat Cleanup: Heal all units. Recall Attackers if Defenders are still present — Defenders are gone (recalled by Hourglass), so Ask's attacker stays. Ask wins combat → Establishes Control → Conquers the battlefield (if not scored yet this turn). Combat ends; Attacker/Defender designations are cleared.

3. Playing Rengar: After combat, the battlefield is controlled by Ask and has Ask's unit there. The opponent can play Rengar, Trophy Hunter to that battlefield because his special permission allows him to Ambush "to a battlefield where there are enemy units, even if you don't have units there" — and Ask's unit is an enemy unit. The opponent would need an appropriate timing window (e.g., a Closed State created by a chain item, or an Open State where they receive priority).

4. New combat designations: When Rengar enters a battlefield the opponent does not control, that player applies Contested status. Per Rule 459.2.b.1, the player whose unit applied Contested is the Attacker. So the opponent (Rengar's controller) becomes the Attacker, and Ask (whose unit was already there) becomes the Defender. This is the reverse of the typical Rengar FAQ scenario — there, the opponent moved first and Rengar entered as Defender; here, Rengar initiates the contest.

In short: Rengar can enter after the Hourglass recall clears the board, and because he's the one applying Contested to a battlefield controlled by Ask, he's the Attacker in the follow-up combat.