To unlock The Gang War trophy in the Turf Wars DLC, you need to complete 5 new Hammerhead crimes in a district. A couple of notes:
-- Only Hell's Kitchen, Upper East Side, Upper West Side and Harlem have Hammerhead crimes; you can ignore the south end of Manhattan.
-- This will only become available after you complete the Jury Rigging main mission, the third main mission in the DLC.
-- You will need to complete all crimes in all above mentioned districts for the below trophy anyway: