Leading Irish father has begun (7)
I believe the answer is:
started
'begun' is the definition.
('start' can be a synonym of 'begin')
'leading irish father' is the wordplay.
'leading' becomes 'star' (synonyms).
'irish father' becomes 'ted' (I can't explain this - if you can you should believe this answer much more).
'star'+'ted'='STARTED'
'has' is the link.
Can you help me to learn more?
(Other definitions for started that I've seen before include "showed surprise" , "Originated" , "kicked-off" , "Began; flinched" , "Made sudden movement from pain or surprise" .)