Right of way can change hands in an instant: a boat finishes her tack, an overlap begins from astern, a boat gybes onto starboard. When you become right-of-way boat through your own action, the other boat gets a moment to respond. You must initially give her room to keep clear, meaning the space and time a competent crew needs to manoeuvre promptly in the conditions.
If you gained right of way because of what the other boat did (she tacked, or she gybed onto port in front of you), rule 15 does not protect her.
"Initially" is short. Once the other boat has had a fair chance to respond, she must keep clear like any keep-clear boat.
Common situations
Overlap to leeward from astern
A boat sailing faster closes from clear astern and becomes overlapped to leeward. She now has right of way under rule 11, but she must give the windward boat room to keep clear. If she arrives so close that windward cannot respond, she breaks rule 15.
Gybing onto starboard
A boat gybes from port to starboard close to a port-tack boat. The moment her boom crosses she has right of way, but the port boat must be given room to respond. A gybe that leaves the port boat no chance breaks rule 15.