Upset to a great degree in certain circumstances (8)
I believe the answer is:
aegrotat
'degree in certain circumstances' is the definition.
(academic degree awarded in certain conditions)
'upset to a great' is the wordplay.
'upset' indicates anagramming the letters.
'to'+'a'+'great'='toagreat'
'toagreat' is an anagram of 'AEGROTAT'.
(Other definitions for aegrotat that I've seen before include "university qualification" , "one who gets through" , "Evidence of university malaise" , "Medical certificate exempting student from exam" .)