A crime for which a clergyman lost his head (5)
I believe the answer is:
arson
'a crime' is the definition.
(crime of illegally starting a fire)
'a clergyman lost his head' is the wordplay.
'a clergyman' becomes 'parson' (parson is a kind of clergyman).
'lost his head' means to remove the first letter.
'parson' with its initial letter removed is 'ARSON'.
'for which' acts as a link.
(Other definitions for arson that I've seen before include "Incendiary act" , "Pyromaniac's crime" , "Fire requiring forensic study" , "Criminal pyromania" , "Crime involving fire" .)