University degree oddly inspired by academic resentment (7)
I believe the answer is:
dudgeon
'resentment' is the definition.
(I've seen this before)
'university degree oddly inspired by academic' is the wordplay.
'university' becomes 'u' (abbreviation for university).
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
'inspired by' indicates putting letters inside (some letters breathed in or 'inspired' by others).
'academic' becomes 'don' (type of academic - especially at Oxbridge).
The alternate letters of 'degree' are 'dge'.
'u'+'dge'='udge'
'udge' inserted into 'don' is 'DUDGEON'.
(Other definitions for dudgeon that I've seen before include "feeling of resentment" , "(High) resentment" , "State of being (highly) aggrieved" , "Sullenness" , "indignant state" .)