By and by girl admits nothing (4)
I believe the answer is:
anon
'by and by' is the definition.
(I've seen this in another clue)
'girl admits nothing' is the wordplay.
'girl' becomes 'ann' (woman's name).
'admits' means one lot of letters goes inside another (to admit is to allow in).
'nothing' becomes 'O' (looks like zero - 0).
'ann' going around 'o' is 'ANON'.
(Other definitions for anon that I've seen before include "In a little while (informal)" , "At another time, of old" , "Without known author" , "Of unknown identity, in short" , "soon to be written" .)