A girl's husband after a wager (4)
I believe the answer is:
beth
'a girl's' is the definition.
'husband after a wager' is the wordplay.
'husband' becomes 'h'.
'after' is a charade indicator (letters next to each other).
'a wager' becomes 'bet' ('bet' can be a synonym of 'wager').
'h' put after 'bet' is 'BETH'.
(Other definitions for beth that I've seen before include "Concluding stanza" , "Meg, Jo, - - and Amy" , "character in Israel" , "letter to the Hebrews" , "Second Hebrew letter" .)