Beheading the cleric is a light crime! (5)
I believe the answer is:
arson
'light crime' is the definition.
'arson' can be an answer for 'crime' (crime of illegally starting a fire). I also know that 'light' relates to this answer.
'beheading the cleric' is the wordplay.
'beheading' means to remove the first letter.
'the cleric' becomes 'parson' (I've seen this in another clue).
'parson' with its first letter removed is 'ARSON'.
'is a' is the link.
(Other definitions for arson that I've seen before include "Malicious burning to destroy property" , "Criminal activity" , "Criminal pyromania" , "Felonious burning of property" , "Torching" .)