Who do pirates hire to hunt pirates? The Men of War, that's who. Those bloody-minded savages are Kidd's own army, and any pirate on the seas who doesn't want to sail under Brethren colors is going to answer to the Men of War. They be the greatest menace to the Caribbean if Kidd didn't keep them under control. Well, barely under control. He feeds them his enemies like feeding a dog scraps. We just hope he doesn't ever run out of enemies.
These cutthroats' sole goal is the eradication of any Pirate Gangs which refuses to join the Brethren proper, lest we have another Dread Saints situation on our hands.
Pirate Reputation maybe gained with them by speaking with the Pirate Hunter's in Cat Island, Golden Lake and of course Tortuga. The Pirate Hunters in those ports have bounties for captains with appropriate experience.