University grant primarily opening door for EU member (8)
I believe the answer is:
portugal
'eu member' is the definition.
(member of European Union)
'university grant primarily opening door' is the wordplay.
'primarily' says to take the initial letters.
'opening' indicates putting letters inside (some letters open a gap in others).
'door' becomes 'portal' (synonyms).
The first letters of 'university grant' is 'ug'.
'ug' going into 'portal' is 'PORTUGAL'.
'for' acts as a link.
(Other definitions for portugal that I've seen before include "Iberian state" , "Iberian country" , "Pluto rag found in the country" , "Westernmost country of mainland Europe" , "Southwest European country" .)