Objective for Indian state that's left behind (4)
I believe the answer is:
goal
'objective' is the definition.
(goal can mean an objective or purpose)
'indian state that's left behind' is the wordplay.
'indian state' becomes 'goa' (Goa is a state of India).
'that's left' becomes 'l' (common abbreviation).
'behind' is a charade indicator (letters next to each other).
'goa'+'l'='GOAL'
'for' is the link.
(Other definitions for goal that I've seen before include "Objective, purpose" , "Aim - two posts, a crossbar and a net" , "posts and bar" , "Footballer's target" , "Aim, desired result" .)