Mythological heroine chosen by artist (7)
I believe the answer is:
electra
'mythological heroine' is the definition.
(heroine in Greek mythology)
'chosen by artist' is the wordplay.
'chosen' becomes 'elect' ('elect' as an adjective can mean chosen).
'by' is a charade indicator (letters next to each other).
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'elect'+'ra'='ELECTRA'
(Other definitions for electra that I've seen before include "Complex parallel to Oedipus" , "King's daughter" , "complex character" , "type of complex" , "heroine of Greece" .)