Minister denied parking offence (5)
I believe the answer is:
arson
'offence' is the definition.
(crime of illegally starting a fire)
'minister denied parking' is the wordplay.
'minister' becomes 'parson' (church minister).
'denied' is a deletion indicator (the word is denied some of its letters).
'parking' becomes 'p' (abbreviation on road signs).
'parson' with 'p' taken out is 'ARSON'.
(Other definitions for arson that I've seen before include "Sonar (anag.)" , "Fire-lighting crime" , "Fire requiring forensic study" , "Incendiarism" , "Iniquitous behaviour" .)