Make a career in China, India or another country (7)
I believe the answer is:
burundi
'another country' is the definition.
'burundi' can be an answer for 'country' (Burundi is an example). I am not certain of the 'another' bit.
'make a career in china india' is the wordplay.
'make a career' becomes 'run' (career can mean to move fast).
'in' is an insertion indicator.
'china' becomes 'bud' (china [plate] is Cockney rhyming slang for 'mate').
'india' becomes 'i' (phonetic alphabet: alpha, bravo, charlie etc.).
'run' going inside 'bud' is 'burund'.
'burund'+'i'='BURUNDI'
'or' acts as a link.
(Other definitions for burundi that I've seen before include "African territory" , "Landlocked African country" , "Central African republic" , "Central African country, capital Bujumbura" , "African state" .)