How do I patch cracked drywall around a ceiling fire sprinkler head without messing up the sprinkler?

First, never apply joint compound directly to the sprinkler assembly or mud the escutcheon ring shut, which can stop it from deploying in a fire. Carefully trim the damaged drywall around the pipe, add wood backing behind the hole, and fit a clean drywall patch while maintaining the required clearance gap around the head. If you need to remove the trim ring or adjust the pipe itself, call a licensed fire protection contractor—snapping that glass bulb under system pressure will flood your room in seconds.