Painter wins over Kensington and Chelsea, say (12)
I believe the answer is:
gainsborough
'painter' is the definition.
(Gainsborough is an example)
'wins over kensington and chelsea say' is the wordplay.
'wins' becomes 'gains' ('gain' can be a synonym of 'win').
'over' means one lot of letters go next to another (in a down clue, some letters go over others).
'kensington and chelsea say' becomes 'borough' (Kensington and Chelsea is a borough of London).
'gains'+'borough'='GAINSBOROUGH'
(Other definitions for gainsborough that I've seen before include "Arty type" , "Lincolnshire town -- 18th-century English painter" , "Artist" , "English portrait and landscape painter, d. 1788" , "Canvasser" .)