Extremely angry about university heads creating stiff examination (7)
I believe the answer is:
autopsy
'stiff examination' is the definition.
(examination of a body or 'stiff')
'extremely angry about university heads' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'about' is an insertion indicator.
'university' becomes 'u' (abbreviation for university).
'heads' becomes 'tops' ().
'angry' with its centre removed is 'ay'.
'u'+'tops'='utops'
'ay' placed around 'utops' is 'AUTOPSY'.
'creating' acts as a link.
(Other definitions for autopsy that I've seen before include "PM" , "Pays out (anag.)" , "final examination" , "Post-mortem inspection" , "Examination after death, a post-mortem" .)