What happens first, Draven's Legend ability (winning combat) or Conquering effect?

Draven's Legend ability triggers and resolves BEFORE conquer effects.

According to the FAQ 'If I win on the attack and conquer, does this happen before or after I score? Before or after conquer effects?':

Draven's ability will trigger and resolve before you gain your regular point for scoring the battlefield and before any conquer effects are triggered.

The sequence is:

1. Combat concludes and you win (only your units remain)
2. Draven's "When you win a combat, draw 1" ability triggers and resolves immediately
3. You gain control of the battlefield (Conquer)
4. Conquer effects trigger and resolve

Important note: This timing matters for the Final Point rule. If you're at 6 points and conquer a battlefield with Draven, you'll draw a card instead of scoring the Final Point—because Draven's draw resolves first, bringing you to 7 points before the conquer effect would trigger.