Minister without portfolio at first gives serious offence (5)
I believe the answer is:
arson
'serious offence' is the definition.
(arson is a crime)
'minister without portfolio at first' is the wordplay.
I cannot really see how this works, but
'at' could be 'on' (location) and 'on' is present in the answer.
'first' could be 'a' (first letter of the alphabet) and 'a' is found in the answer.
This explanation may well be incorrect...
'gives' is the link.
(Other definitions for arson that I've seen before include "burning problem" , "Torching" , "serious offence" , "It may get you in court" , "Malicious fire-raising" .)