Oriental cuisine's finale: a small bird (7)
I believe the answer is:
Here is my best explanation:
'oriental' is the definition.
('eastern' can be a synonym of 'oriental')
'cuisine's finale a small bird' is the subsidiary indication.
'finale' indicates one should take the final letters.
'small' becomes 's' (abbreviation - e.g. clothes size).
'bird' becomes 'tern' (tern is a kind of bird**).
The last letter of 'cuisine' is 'e'.
(Other definitions for eastern that I've seen before include "Coming from the Orient", "Could be Chinese", "Maybe Chinese", "from afar", "Nearest (anag) - oriental", "Earnest (anag.)", "in Beijing, possibly", "Possibly Japanese", "China?" and "towards the sun".)