Universal anger shown about doctor's offence (7)
I believe the answer is:
umbrage
'offence' is the definition.
(I've seen this before)
'universal anger shown about doctor's' is the wordplay.
'universal' becomes 'u'.
'anger' becomes 'rage' (rage is a kind of anger).
'shown about' means one lot of letters goes inside another.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus).
'u'+'rage'='urage'
'urage' going around 'mb' is 'UMBRAGE'.
(Other definitions for umbrage that I've seen before include "Feeling of anger caused by being offended" , "Resentment, offence" , "Offence that's usually taken" , "Take this to feel offence" , "In high dudgeon" .)