The master's won round by her (5)
I believe the answer is:
woman
'her' is the definition.
('her' refers to a woman)
'the master's won round' is the wordplay.
'the master' becomes 'MA' (Master of Arts).
'round' means one lot of letters goes inside another.
'ma' put inside 'won' is 'WOMAN'.
'by' acts as a link.
(Other definitions for woman that I've seen before include "Mature female" , "With 1a [OLD], one's rather timid" , "With 1a [NEW] a freedom fighter" , "Lady" , "See 16" .)