The Access Code says:
Access rights extend to climbing. Follow any agreements between a land manager and recreational groups that seek, for example, to safeguard a rare bird nesting site (such an agreement might ask you not to climb particular crags or sections of crags during the breeding season).
If you are camping close to a crag, follow the guidance for wild camping.
The Mountaineering Council for Scotland provides advice on where climbing crags are affected by breeding birds. They also issue guidance for climbers about climbing and nesting birds as well as information about other likely species climbers could encounter whilst enjoying their sport.