Criticise artist holding party for Greek woman (7)
I believe the answer is:
pandora
'greek woman' is the definition.
(figure of Greek myth)
'criticise artist holding party' is the wordplay.
'criticise' becomes 'pan' (informal term meaning to criticise heavily).
'artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts).
'holding' is an insertion indicator.
'party' becomes 'do' (do is a kind of party).
'pan'+'ra'='panra'
'panra' going around 'do' is 'PANDORA'.
'for' is the link.
(Other definitions for pandora that I've seen before include "Her mythical box was filled with evil" , "Inquisitive woman who opened a box" , "First mortal woman of Greek mythology" , "Adrian Mole's love; box-of-troubles girl" , "Her box was filled with all the ills of the world" .)