Very unpromising offer to accept right winger (9)
I believe the answer is:
blackbird
'winger' is the definition.
(something with wings)
'very unpromising offer to accept right' is the wordplay.
'very unpromising' becomes 'black' (black can mean inauspicious or unlucky).
'offer' becomes 'bid' ('bid' can be a synonym of 'offer').
'to accept' is an insertion indicator.
'right' becomes 'r' (common abbreviation).
'bid' enclosing 'r' is 'bird'.
'black'+'bird'='BLACKBIRD'
(Other definitions for blackbird that I've seen before include "slave on ship" , "garden pecker pecker" , "It has a yellow bill" , "Relative of thrush" , "One of 24 in pie" .)