Infuriated with hair (3)
I believe the answer is:
fur
'hair' is the definition.
(I know that fur is a type of coat)
'infuriated with' is the wordplay.
'with' indicates a hidden word.
'FUR' is hidden in the letters of 'infuriated'.
(Other definitions for fur that I've seen before include "Coating in kettle" , "Mink or ermine, say" , "Deposit inside kettles" , "Outer skin of animal with hair attached" , "Eg, sable or ermine" .)