Start celebrating part coming up in this Greek tragedy (7)
I believe the answer is:
electra
'this greek tragedy' is the definition.
(I've seen this before)
'start celebrating part coming up' is the wordplay.
'part' says the answer is hidden in the clue.
'coming up' is a reversal indicator (in a down clue, letters go up).
'artcele' can be found hidden inside 'start celebrating'.
'artcele' written backwards gives 'ELECTRA'.
'in' acts as a link.
(Other definitions for electra that I've seen before include "Mythical woman with a complex?" , "Treacle (anag) - daughter of Agamemnon" , "titled lady" , "She sought vengeance" , "Sort of complex" .)