Complex woman's chosen academician (7)
I believe the answer is:
electra
'complex woman's' is the definition.
(woman after whom the Electra Complex is named)
'chosen academician' is the wordplay.
'chosen' becomes 'elect' ('elect' as an adjective can mean chosen).
'academician' becomes 'RA' (member of the Royal Academy of Arts).
'elect'+'ra'='ELECTRA'
(Other definitions for electra that I've seen before include "Greek tragedy" , "Complex parallel to Oedipus" , "mythological princess" , "Mythical woman with a complex?" , "titled lady" .)