Pirate Hunter is a common mission that can be found in the Tavern's Side Room.
You will receive a map that shows the location of a pirate. If any of your ships passes the spot, it will be attacked by the pirate. The reward offered indicates the type of the pirate ship, larger reward means larger pirate ship.
One such mission is always available in the Hanse at any given moment, as long as you haven't accepted one already.