Elite artist is complex woman (7)
I believe the answer is:
electra
'complex woman' is the definition.
(woman after whom the Electra Complex is named)
'elite artist' is the wordplay.
'elite' becomes 'elect' (elect is a kind of elite).
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'elect'+'ra'='ELECTRA'
'is' is the link.
(Other definitions for electra that I've seen before include "Daughter of Agamemnon and Clytemnestra (who has a complex?)" , "Greek heroine (with a complex!)" , "Complex parallel to Oedipus" , "Complex female" , "Greek tragedy" .)