Greek character’s crumbling pen outside farm store (7)
I believe the answer is:
epsilon
'greek character's' is the definition.
(letter from the Greek alphabet)
'crumbling pen outside farm store' is the wordplay.
'crumbling' is an anagram indicator.
'outside' is an insertion indicator.
'farm store' becomes 'silo' (store for grain).
'pen' is an anagram of 'epn'.
'epn' placed around 'silo' is 'EPSILON'.
(Other definitions for epsilon that I've seen before include "character in Greece" , "small number mispronounced, almost completely the wrong way round" , "foreign letter" , "Greek letter E" , "Greek letter - pinoles (anag)" .)