Crime of minister initially denied (5)
I believe the answer is:
arson
'crime' is the definition.
(crime of illegally starting a fire)
'minister initially denied' is the wordplay.
'minister' becomes 'parson' (church minister).
'initially denied' means to remove the first letter (the word is denied its initial).
'parson' with its initial letter taken off is 'ARSON'.
'of' is the link.
(Other definitions for arson that I've seen before include "serious offence" , "Iniquitous behaviour" , "criminal fire-raising" , "Crime involving fire" , "burning problem" .)