Nipper starts to dance happily in Irish music festival (6)
I believe the answer is:
fleadh
'irish music festival' is the definition.
(Fleadh Cheoil)
'nipper starts to dance happily' is the wordplay.
'nipper' becomes 'flea'.
'starts to' suggests taking the first letters.
The initial letters of 'dance happily' is 'dh'.
'flea'+'dh'='FLEADH'
'in' is the link.
(Other definitions for fleadh that I've seen before include "Irish festival" , "festival in Cork?" .)