Record store never opening letter from Greece (7)
I believe the answer is:
epsilon
'letter from greece' is the definition.
(letter from the Greek alphabet)
'record store never opening' is the wordplay.
'record' becomes 'EP' (abbreviation for extended play record).
'store' becomes 'silo' (a store of crops).
'opening' indicates taking the first letters.
The first letter of 'never' is 'n'.
'ep'+'silo'+'n'='EPSILON'
(Other definitions for epsilon that I've seen before include "Greek letter E" , "character in Greece" , "foreign letter" , "Fifth letter of the Greek alphabet" , "Fifth brightest star in a constellation" .)