Choose Royal Academy to present Greek tragedy (7)
I believe the answer is:
electra
'greek tragedy' is the definition.
(I've seen this before)
'choose royal academy' is the wordplay.
'choose' becomes 'elect' (electing is a kind of choosing).
'royal academy' becomes 'ra'.
'elect'+'ra'='ELECTRA'
'to present' is the link.
(Other definitions for electra that I've seen before include "Complex girl" , "complex character" , "Sort of complex" , "Treacle (anag) - daughter of Agamemnon" , "Greek heroine (with a complex!)" .)