Choose artist for legendary Greek daughter (7)
I believe the answer is:
electra
'legendary greek daughter' is the definition.
(I've seen this before)
'choose artist' is the wordplay.
'choose' becomes 'elect' (electing is a kind of choosing).
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'elect'+'ra'='ELECTRA'
'for' is the link.
(Other definitions for electra that I've seen before include "Mourning Becomes ____ (play cycle Eugene O'Neill)" , "vengeful daughter" , "Treacle (anag) - daughter of Agamemnon" , "Greek heroine (with a complex!)" , "titled lady" .)