Chosen artist is complex woman? (7)
I believe the answer is:
electra
'complex woman?' is the definition.
(woman after whom the Electra Complex is named)
'chosen artist' is the wordplay.
'chosen' becomes 'elect' ('elect' as an adjective can mean chosen).
'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 "mythological princess" , "Treacle (anag) - daughter of Agamemnon" , "Mythical woman with a complex?" , "She sought vengeance" , "complex character" .)