Single university attended by fool (4)
I believe the answer is:
unit
'single' is the definition.
('unit' can be a synonym of 'single')
'university attended by fool' is the wordplay.
'university' becomes 'u'.
'attended by' says to put letters next to each other.
'fool' becomes 'nit' (I've seen this before).
'u'+'nit'='UNIT'
(Other definitions for unit that I've seen before include "Individual thing as part of a whole" , "Element or part" , "Some fighting men" , "Entity making up part of a whole" , "1 entity" .)