Lady succeeded ultimately, having superior game (7)
I believe the answer is:
duchess
'lady' is the definition.
(duchess is a kind of lady)
'succeeded ultimately having superior game' is the wordplay.
'ultimately' indicates one should take the final letters.
'having' means one lot of letters go next to another.
'superior' becomes 'u' (I've seen this in other clues).
'game' becomes 'chess' (chess is a kind of game**).
The final letter of 'succeeded' is 'd'.
'd'+'u'+'chess'='DUCHESS'
(Other definitions for duchess that I've seen before include "title" , "Wife of a duke" , "Noble lady" , "Titled female" , "Noblewoman" .)