Lady Katrine Raven is the leader of the Black Arm Gang. She has quite a temper and is located in the Black Arm Gang headquarters, just to the west in an alleyway as you enter Varrock via its southern gate.
She asks players wanting to join her gang to give her two Phoenix Gang crossbows as a test of skill and loyalty to her. Katrine will also refuse entry and would spit at any player who is a member of the Phoenix Gang that tries to talk to her.
Once you have joined her gang you must team up with another member not in the Black Arm Gang in order to infiltrate the Phoenix Gang so that you both may complete the quest.