Travelled through part of Ireland, avoiding Castlebar, finally, and Pontoon (6-3)
I believe the answer is:
twenty-one
'pontoon' is the definition.
(names for the same card game)
'travelled through part of ireland avoiding' is the wordplay.
'travelled' becomes 'twenty' (I can't justify this - if you can you should believe this answer much more).
'through' becomes 'by'.
'part of ireland' becomes 'Boyne' (Irish river).
'avoiding' is a deletion indicator.
'boyne' with 'by' removed is 'one'.
'twenty'+'one'='TWENTY-ONE'
'castlebar finally and' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.
(Other definitions for twenty-one that I've seen before include "Card game, blackjack or pontoon" , "Target total in blackjack or pontoon" , "XXI - used to be the coming of age year" .)