Irishman bringing post around (4)
I believe the answer is:
liam
'irishman' is the definition.
(common Irish name)
'post around' is the wordplay.
'post' becomes 'mail' (synonyms).
'around' shows that the letters should be reversed in order.
'mail' written backwards gives 'LIAM'.
'bringing' is the link.
(Other definitions for liam that I've seen before include "Boy" , "-- Neeson (actor)" , "Irishman" .)