Clergyman loses head for crime (5)
I believe the answer is:
arson
'crime' is the definition.
(I've seen this before)
'clergyman loses head' is the wordplay.
'clergyman' becomes 'parson' (parson is a kind of clergyman).
'loses head' means to remove the first letter.
'parson' with its initial letter taken away is 'ARSON'.
'for' is the link.
(Other definitions for arson that I've seen before include "Felonious burning of property" , "Fire-raising crime" , "Crime of fire raising" , "Incendiary act" , "Criminal activity" .)