Head Dane off (4)
I believe the answer is:
dean
'head' is the definition.
(dean is a kind of head)
'dane off' is the wordplay.
'off' indicates anagramming the letters.
'dane' anagrammed gives 'DEAN'.
(Other definitions for dean that I've seen before include "Cathedral cleric" , "James ..., film actor" , "Jonathan Swift's occupation" , "Head of e.g. faculty" , "Senior academic administrator" .)