Award daughter, for one, always rejected (6)
I believe the answer is:
degree
'award' is the definition.
(degree is a kind of award)
'daughter for one always rejected' is the wordplay.
'daughter' becomes 'd'.
'for one' becomes 'eg' (I've seen this in other clues).
'always' becomes 'eer' (poetic way of saying ever).
'rejected' says the letters should be written in reverse.
'eer' backwards is 'ree'.
'd'+'eg'+'ree'='DEGREE'
(Other definitions for degree that I've seen before include "Angular unit; grade" , "Angular unit and college award" , "Not much of a turn" , "'Grade, step or award (6)'" , "Educational qualification" .)