Proverb influencing wife to leave (6)
I believe the answer is:
saying
'proverb' is the definition.
(thesaurus)
'influencing wife to leave' is the wordplay.
'influencing' becomes 'swaying' (swaying is a kind of influencing).
'wife' becomes 'w'.
'to leave' suggests deleting specific letters.
'swaying' with 'w' taken out is 'SAYING'.
(Other definitions for saying that I've seen before include "Adage, maxim" , "Expressing in words" , "Uttering" , "talking!" , "Saw" .)