Obligation of first appearance leaving university (4)
I believe the answer is:
debt
'obligation' is the definition.
('debt' can be a synonym of 'obligation')
'of first appearance leaving university' is the wordplay.
'of' becomes 'o'.
'first appearance' becomes 'debut' ('debut' can be a synonym of 'first appearance').
'leaving' indicates named letters should be taken away.
'university' becomes 'ou'.
'o'+'debut'='odebut'
'odebut' with 'ou' removed is 'DEBT'.
(Other definitions for debt that I've seen before include "Amount owed" , "Financial problem?" , "Amount owing" , "Arrears, liability" , "Liability, obligation" .)