I looked at my notes, since I have recently gone over these quests for the wiki, and my notes show that after seeing William Turk, he directs you to sink some Navy ships.
The Liberation of the Black Pearl
Story Chapter: The Black Pearl
Right Greer's Wrongs
William Turk
Sink Navy Ships - Sink 8 Navy ships. (0/8)
Then he sends you to see Doc Grog.