This can be a key issue. If you have spotted something on the reef then instead of heading straight at it, take a few moments to watch how it behaves and what it does. Approach it from the side not head on and slowly with no sudden movements. Check out the area around it and find a place you can rest safely without damaging the reef. Let it/them get used to you before you take your shots.
Some subjects may become inquisitive and move closer to you if you remain still. This is true of Butterfly fish, Angel fish, Trumpet fish and Wrasse. I have often experienced Angel fish swim very close to my lens whilst composing a reef or wreck shot, which creates a stunning focus point at the front of the photograph. They don’t hand around for long though and I only manage to get off a couple of photos.