Pick British artist to appear in Greek play (7)
I believe the answer is:
electra
'greek play' is the definition.
'electra' can be an answer for 'play' (I've seen this before). I'm not certain of the 'greek' bit.
'pick british artist' is the wordplay.
'pick' becomes 'elect' (to elect is to pick or select).
'british artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts. I am not sure about the 'british' bit.).
'elect'+'ra'='ELECTRA'
'to appear in' acts as a link.
Can you help me to learn more?
(Other definitions for electra that I've seen before include "Female avenger" , "It's a kind of complex" , "Tragic daughter of Agamemnon" , "Mourning Becomes ____ (play cycle Eugene O'Neill)" , "mythological princess" .)