Head off donkey in a whirl (4)
I believe the answer is:
eddy
'a whirl' is the definition.
(thesaurus)
'head off donkey' is the wordplay.
'head off' means to remove the first letter.
'donkey' becomes 'neddy' (I've seen this before).
'neddy' with its initial letter removed is 'EDDY'.
'in' acts as a link.
(Other definitions for eddy that I've seen before include "movement going round in circles" , "Swirl; small whirlpool" , "Vortex" , "Current running against the main stream, causes small whirlpool" , "Swirl; Duane -, US guitarist" .)