Noblewoman finally cooked high-class game (7)
I believe the answer is:
duchess
'noblewoman' is the definition.
(duchess is a kind of noblewoman)
'finally cooked high-class game' is the wordplay.
'finally' indicates one should take the final letters.
'high class' becomes 'U' (as in U and non-U speech).
'game' becomes 'chess' (board game).
The last letter of 'cooked' is 'd'.
'd'+'u'+'chess'='DUCHESS'
(Other definitions for duchess that I've seen before include "Duke's wife" , "Noble lady" , "Wife of a duke" , "Female aristocrat" , "Titled lady" .)