Girl denied son's become boxer (3)
I believe the answer is:
ali
'boxer' is the definition.
(Muhammad Ali)
'girl denied son's' is the wordplay.
'girl' becomes 'Alison' (girl's name).
'denied' indicates named letters should be taken away (the word is denied or deprived of certain letters).
'alison' with 'son' removed is 'ALI'.
'become' is the link.
(Other definitions for ali that I've seen before include "Muhammad's son-in-law" , "Muhammad or Baba?" , "Muslim name" , "Mohammed . . . (boxer)" , "Old fighter" .)