Show-off regrets work that's been rejected (6)
I believe the answer is:
poseur
'show-off' is the definition.
(poseur is a kind of show-off)
'regrets work that's been rejected' is the wordplay.
'regrets' becomes 'rues' ('rue' can be a synonym of 'regret').
'work' becomes 'op' (common abbreviation for 'opus').
'that's been rejected' shows that the letters should be reversed in order.
'rues'+'op'='ruesop'
'ruesop' reversed gives 'POSEUR'.
(Other definitions for poseur that I've seen before include "Uprose (anag.)" , "Person who's affected" , "Pretentious person" , "One shows off to impress" , "One behaving affectedly to impress others" .)