Noblewoman’s daughter beginning to understand board game (7)
I believe the answer is:
duchess
'noblewoman's' is the definition.
(duchess is a kind of noblewoman)
'daughter beginning to understand board game' is the wordplay.
'daughter' becomes 'd'.
'beginning to' suggests taking the first letters.
'board game' becomes 'chess' (chess is a kind of board game).
The first letter of 'understand' is 'u'.
'd'+'u'+'chess'='DUCHESS'
(Other definitions for duchess that I've seen before include "Duke's wife" , "Wife of a duke" , "Great lady" , "title" , "Noblewoman" .)