Offence of minister losing head? (5)
I believe the answer is:
arson
'offence' is the definition.
(I've seen this before)
'minister losing head?' is the wordplay.
'minister' becomes 'parson' ('parson' can be a synonym of 'minister').
'losing head?' means to remove the first letter.
'parson' with its first letter taken away is 'ARSON'.
'of' is the link.
(Other definitions for arson that I've seen before include "Be pettish" , "Crime of fire setting" , "major crime" , "Felonious burning of property" , "criminal fire-raising" .)