Parish priest ignoring first offence (5)
I believe the answer is:
arson
'offence' is the definition.
(crime of illegally starting a fire)
'parish priest ignoring first' is the wordplay.
'parish priest' becomes 'parson'.
'ignoring first' means to remove the first letter.
'parson' with its initial letter removed is 'ARSON'.
(Other definitions for arson that I've seen before include "Malicious fire-lighting" , "Malicious burning to destroy property" , "Act of a pyromaniac" , "A burning crime" , "Pyromaniac's crime" .)