Crossword Genius

Lady Diana's first university game (7)

Ross

I believe the answer is:

duchess

'lady' is the definition.
(I know that duchess is a type of lady)

'diana's first university game' is the wordplay.
'diana's first' becomes 'd' (1st letter of 'diana').
'university' becomes 'U' (abbreviation for university).
'game' becomes 'chess' (board game).
'd'+'u'+'chess'='DUCHESS'

(Other definitions for duchess that I've seen before include "Titled female" , "Titled lady" , "Great lady" , "Duke's wife" , "Noble lady" .)

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