Draw tart cat demolished (7)
I believe the answer is:
attract
'draw' is the definition.
(I know that draw can be written as attract)
'tart cat demolished' is the wordplay.
'demolished' indicates an anagram.
'tart'+'cat'='tartcat'
'tartcat' anagrammed gives 'ATTRACT'.
(Other definitions for attract that I've seen before include "Exert a pull upon" , "to be appealing" , "Entrance" , "Draw towards, being magnetic" , "Draw towards like a magnet" .)