Old Irishman is an emigre (5)
I believe the answer is:
expat
'an emigre' is the definition.
(I've seen this before)
'old irishman' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'irishman' becomes 'Pat' (Patrick is a common Irish name).
'ex'+'pat'='EXPAT'
'is' is the link.
(Other definitions for expat that I've seen before include "resident abroad" , "overseas settler" , "who now uses overseas address?" , "Degrade" , "Person living abroad" .)