I'm going to stop working in American university (5)
I believe the answer is:
adieu
'i'm going' is the definition.
(I've seen this before)
'stop working in american university' is the wordplay.
'stop working' becomes 'die' (I've seen this in other clues).
'in' is an insertion indicator.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'university' becomes 'U' (abbreviation for university).
'a'+'u'='au'
'die' going inside 'au' is 'ADIEU'.
'to' is the link.
(Other definitions for adieu that I've seen before include "So long abroad" , "12 Down" , "Ciao, in French" , "A valediction" , "Farewell, ami!" .)