Finished training after Irish backs, past their best? (8)
I believe the answer is:
overripe
'past their best?' is the definition.
(no longer ripe)
'finished training after irish backs' is the wordplay.
'finished' becomes 'over' (similar in meaning).
'training' becomes 'PE' (Physical Education).
'after' means one lot of letters go next to another.
'irish' becomes 'IR' (abbreviation).
'backs' says the letters should be written in reverse.
'ir' reversed gives 'ri'.
'pe' after 'ri' is 'ripe'.
'over'+'ripe'='OVERRIPE'
(Other definitions for overripe that I've seen before include "(Of fruit, cheese, etc) past the usual stage for eating" , "I reprove for being too mature" , "(Of fruit) past its best" , "More than ready" , "More than mature, fruit say" .)