Festival that's not completely oriental (6)
I believe the answer is:
easter
'festival' is the definition.
(Christian festival)
'not completely oriental' is the wordplay.
'not completely' means to remove the last letter (the word is incomplete).
'oriental' becomes 'eastern' (similar in meaning).
'eastern' with its final letter taken away is 'EASTER'.
'that's' acts as a link.
(Other definitions for easter that I've seen before include "- Day; - bunny" , "A steer (anag.)" , "Main Christian festival" , "Resurrection festival" , "Christian celebration of the Resurrection" .)