Indian state importing high-class, primarily Dutch, cheese (5)
I believe the answer is:
gouda
'cheese' is the definition.
(I know that Gouda is a type of cheese)
'indian state importing high-class primarily dutch' is the wordplay.
'indian state' becomes 'goa' (Goa is a state of India).
'importing' means one lot of letters goes inside another.
'high class' becomes 'U' (as in U and non-U speech).
'primarily' says to take the initial letters.
The initial letter of 'dutch' is 'd'.
'u'+'d'='ud'
'goa' enclosing 'ud' is 'GOUDA'.
(Other definitions for gouda that I've seen before include "Mild Dutch cheese" , "It comes from Holland" , "Round Dutch cheese" , "type of cheese" , "Dutch town" .)