Woman is con artist (4)
I believe the answer is:
dora
'woman' is the definition.
'con artist' is the wordplay.
'con' becomes 'do' (to 'do' someone could be to con them).
'artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts).
'do'+'ra'='DORA'
'is' acts as a link.
(Other definitions for dora that I've seen before include "Bryan" , "David Copperfield's 'child-wife'" , "This girl" .)