Crime sees religious minister lose head (5)
I believe the answer is:
arson
'crime' is the definition.
(crime of illegally starting a fire)
'minister lose head' is the wordplay.
'minister' becomes 'parson' (church minister).
'lose head' means to remove the first letter (lose (remove) the head (start) of the word).
'parson' with its initial letter taken away is 'ARSON'.
'sees religious' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for arson that I've seen before include "Act of a pyromaniac" , "Torching" , "Malicious fire-raising" , "Incendiary act" , "serious offence" .)