Slight but not trivial offence (7)
I believe the answer is:
affront
I believe this clue is a double definition.
'slight' is the first definition.
(both can mean to offend)
'not trivial offence' is the second definition.
(I've seen this before)
'but' acts as a link.
(Other definitions for affront that I've seen before include "Insult openly" , "Snub" , "Open insult" , "provocation" , "Indignity" .)