Country off India (3,5)
I believe the answer is:
sri lanka
'country off india' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for sri lanka that I've seen before include "It used to be called Ceylon" , ""The teardrop of India"" , "Country off the southeast coast of India" , "Former Ceylon" , "Country south of India" .)