Wife quits golf club in bitterness (4)
I believe the answer is:
edge
'bitterness' is the definition.
(thesaurus)
'wife quits golf club' is the wordplay.
'wife' becomes 'w'.
'quits' is a deletion indicator.
'golf club' becomes 'wedge' (type of golf club).
'wedge' with 'w' taken away is 'EDGE'.
'in' acts as a link.
(Other definitions for edge that I've seen before include "Margin, outside limit" , "Margin, fringe" , "Bind" , "Creep" , "Outer limit" .)