Most important popular cook outside India (2-5)
I believe the answer is:
in-chief
'most important' is the definition.
(as in an editor-in-chief)
'popular cook outside india' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'cook' becomes 'chef' (both can mean someone who cooks).
'outside' is an insertion indicator.
'india' becomes 'i' (phonetic alphabet: alpha, bravo, charlie etc.).
'chef' placed around 'i' is 'chief'.
'in'+'chief'='IN-CHIEF'
(Other definitions for in-chief that I've seen before include "Most importantly" , "Highest in rank" .)