Argue angrily about doctor's offence (7)
I believe the answer is:
umbrage
'offence' is the definition.
(I've seen this before)
'argue angrily about doctor's' is the wordplay.
'angrily' is an anagram indicator (I've seen this in other clues).
'about' is an insertion indicator.
'doctor' becomes 'MB' (Bachelor of Medicine, Medicinae Baccalaureus).
'argue' anagrammed gives 'urage'.
'urage' enclosing 'mb' is 'UMBRAGE'.
(Other definitions for umbrage that I've seen before include "It''s given or taken in offence" , "Displeasure" , "Offence, annoyance" , "Take this to feel offence" , "Feeling of anger caused by being offended" .)