Drunken shag in University leads to distress (7)
I believe the answer is:
anguish
'to distress' is the definition.
(anguish is a kind of distress)
'drunken shag in university leads' is the wordplay.
'drunken' is an anagram indicator.
'leads' says to take the initial letters.
The initial letter of 'university' is 'u'.
'shag'+'in'+'u'='shaginu'
'shaginu' is an anagram of 'ANGUISH'.
(Other definitions for anguish that I've seen before include "Severe mental suffering" , "Agony, distress" , "Severe pain, physical or mental" , "Severe pain, may be mental" , "Angst" .)