Quatrain, oddly, rejected in Middle Eastern country (4)
I believe the answer is:
iraq
'middle eastern country' is the definition.
(I've seen this before)
'quatrain oddly rejected' is the wordplay.
'oddly' means one should take alternating letters.
'rejected' says the letters should be written backwards.
The alternate letters of 'quatrain' are 'qari'.
'qari' back-to-front is 'IRAQ'.
'in' acts as a link.
(Other definitions for iraq that I've seen before include "Present-day site of Mesopotamia" , "Mosul's country" , "troubled state" , "Country containing ancient Mesopotamia" , "Basra's country" .)