One who succeeds among the Irish (4)
I believe the answer is:
heir
'one who succeeds' is the definition.
(I've seen this in another clue)
'among the irish' is the wordplay.
'among' indicates the answer is hidden within the clue.
'HEIR' is hidden within 'the irish'.
(Other definitions for heir that I've seen before include "One who will succeed to title" , "The first boy maybe" , "Son, say" , "Someone expected to inherit" , "Treasured family possession" .)