Defeat a hard nut, did you say? (7)
I believe the answer is:
conquer
'defeat' is the definition.
(conquering is a kind of defeating)
'a hard nut did you say?' is the wordplay.
'a hard nut' becomes 'conker' (nut of the horse chestnut tree).
'did you say?' shows a homophone (sound like).
'conker' sounds like 'CONQUER'.
(Other definitions for conquer that I've seen before include "Act like William" , "Be victorious" , "Triumph over" , "Overcome militarily" , "Climb (a mountain)" .)