The Irish will welcome a person who succeeds (4)
I believe the answer is:
heir
'a person who succeeds' is the definition.
(I've seen this before)
'the irish will welcome' is the wordplay.
'welcome' indicates a hidden word (I've seen 'welcoming' mean this).
'HEIR' is hidden in the letters of 'the irish will'.
(Other definitions for heir that I've seen before include "Beneficiary, inheritor" , "Natural successor" , "One who succeeds" , "One hoping to succeed" , "Expected successor" .)