Mention Kindle former wife dropped (4)
I believe the answer is:
cite
'mention' is the definition.
('cite' can be a synonym of 'mention')
'kindle former wife dropped' is the wordplay.
'kindle' becomes 'excite' (exciting is a kind of kindling).
'former wife' becomes 'ex'.
'dropped' suggests deleting specific letters.
'excite' with 'ex' taken out is 'CITE'.
(Other definitions for cite that I've seen before include "name" , "for instance" , "Quote (a reference)" , "Make reference to" , "Adduce as proof" .)