Kept woman as cure, not remedy (9)
'kept woman' is the definition.
(courtesan is a kind of kept woman)
'as cure not remedy' is the wordplay.
'remedy' is an anagram indicator (I've seen this in other clues).
'ascurenot' is an anagram of 'COURTESAN'.
(Other definitions for courtesan that I've seen before include "loose woman", "lover", "odalisque", "High-class prostitute", "Kept woman".)