Beheading a clergyman is a serious crime (5)
I believe the answer is:
arson
'a serious crime' is the definition.
(crime of starting a fire)
'beheading a clergyman' is the wordplay.
'beheading' means to remove the first letter.
'a clergyman' becomes 'parson' (parson is a kind of clergyman).
'parson' with its first letter taken away is 'ARSON'.
'is' acts as a link.
(Other definitions for arson that I've seen before include "criminal fire-raising" , "Incendiary act" , "Criminal pyromania" , "Malicious crime" , "Fire-raising crime" .)