This side quest unlocks after completing the "...Everything is Permitted" main quest. To begin this quest, you must return to the tavern in Great Inagua. This will trigger a cutscene showing a meeting between Edward and Lieutenant Maynard, who killed Thatch.
Return to Great Inagua and raise a glass for Thatch.

1. Talk to Anne Bonny
Anne is waiting for you on the pier so simply head over to her.

2. Walk with Anne Bonny
Anne will want to speak with you in private. Follow her toward your ship, board it, and approach the captain's cabin entrance. A cutscene will trigger in which Edward shares his plans with Anne - after which this quest will end and the next one - Not Even a Real Captain - will start automatically.
