Backed local voting area appeal (4)
I believe the answer is:
draw
'appeal' is the definition.
(draw can mean appeal or attraction)
'backed local voting area' is the wordplay.
'backed' says the letters should be written backwards.
'local voting area' becomes 'ward' (subdivision of an area for electoral purposes).
'ward' reversed gives 'DRAW'.
(Other definitions for draw that I've seen before include "Make lines on a surface" , "Depict - raffle" , "Sketch; attraction" , "Drag" , "attractive thing" .)