Clergyman has no head for crime (5)
I believe the answer is:
arson
'for crime' is the definition.
(crime of illegally starting a fire)
'clergyman has no head' is the wordplay.
'clergyman' becomes 'parson' (parson is a kind of clergyman).
'has no head' means to remove the first letter.
'parson' with its initial letter taken away is 'ARSON'.
(Other definitions for arson that I've seen before include "Malicious fire-lighting" , "Criminal activity" , "Pyromaniac crime" , "Sonar (anag.)" , "Fire-raising crime" .)