Minister quietly denied crime (5)
I believe the answer is:
arson
'crime' is the definition.
(crime of illegally starting a fire)
'minister quietly denied' is the wordplay.
'minister' becomes 'parson' (church minister).
'quietly' becomes 'p' (p for piano and quiet).
'denied' is a deletion indicator.
'parson' with 'p' taken out is 'ARSON'.
(Other definitions for arson that I've seen before include "A burning crime" , "Incendiarism" , "Malicious fire-raising" , "Pyromaniac crime" , "Torching" .)