Counter-conditioning
Changing what something predicts, so the animal's feeling about it changes — the nail clippers stop meaning restraint and start meaning chicken.
Training a different behaviour on top of fear does not remove the fear; it puts a lid on it. Counter-conditioning goes underneath, by pairing the frightening thing with something good until the frightening thing itself becomes the cue for good news. The order matters: the trigger appears first, the food follows. Reverse it and you have taught the animal that food predicts the scary thing.
It is almost always run alongside desensitisation, because the pairing only works at an intensity the animal can still eat at. An animal too frightened to take food is over threshold, and the session has stopped teaching anything.