Could be Chinese food mainly at the back (3,7)
I believe the answer is:
far eastern
'could be chinese' is the definition.
(China is a country of the far east)
'food mainly at the back' is the wordplay.
'food' becomes 'fare' (fare is a kind of food).
'mainly' means to remove the last letter.
'the back' becomes 'stern' (stern is a kind of back).
'at' with its final letter removed is 'a'.
'fare'+'a'+'stern'='FAR EASTERN'
(Other definitions for far eastern that I've seen before include "from Japan, say?" , "Chinese?" , "from the Orient" , "Perhaps Japanese" .)