Former partner with postman living abroad (5)
I believe the answer is:
expat
'living abroad' is the definition.
(I've seen this before)
'former partner with postman' is the wordplay.
'former partner' becomes 'ex' (an ex-partner).
'with' says to put letters next to each other.
'postman' becomes 'pat' (children's TV character Postman Pat).
'ex'+'pat'='EXPAT'
(Other definitions for expat that I've seen before include "who now uses overseas address?" , "he has emigrated" , "Person living abroad" , "One who lives abroad" , "resident abroad" .)