Kent town's embracing eastern food (10)
I believe the answer is:
sandwiches
'food' is the definition.
(I know that sandwiches is a type of finger food)
'kent town's embracing eastern' is the wordplay.
'kent town's' becomes 'Sandwich's' (town in Kent).
'embracing' means one lot of letters goes inside another.
'eastern' becomes 'e'.
'sandwichs' enclosing 'e' is 'SANDWICHES'.
(Other definitions for sandwiches that I've seen before include "submarines?" , "Quick food" .)