Nut overcome, reportedly? (6)
I believe the answer is:
conker
'nut' is the definition.
(the nut of a horse chestnut tree)
'overcome reportedly?' is the wordplay.
'overcome' becomes 'conquer' (conquering is a kind of overcoming).
'reportedly?' indicates a 'sounds like' (homophone) clue (I've seen 'reportedly' mean this).
'conquer' sounds like 'CONKER'.
(Other definitions for conker that I've seen before include "hard nut" , "Seed of horse chestnut" , "Chestnut on a string" , "Nut of the horse chestnut tree" , "Chestnut fruit" .)