Universal anger about doctor's offence (7)
I believe the answer is:
umbrage
'offence' is the definition.
(I know that offence can be written as umbrage)
'universal anger about doctor's' is the wordplay.
'universal' becomes 'u'.
'anger' becomes 'rage' (rage is a kind of anger).
'about' means one lot of letters go next to another.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'rage' after 'mb' is 'mbrage'.
'u'+'mbrage'='UMBRAGE'
(Other definitions for umbrage that I've seen before include "Offence that's usually taken" , "Take this to feel offence" , "Offence, annoyance" , "The sulks" , "Feeling of offence" .)