A short distance divides Greek and Arab school (7)
I believe the answer is:
grammar
'school' is the definition.
(grammar school is a kind of school)
'a short distance divides greek and arab' is the wordplay.
'short distance' becomes 'mm' (abbreviation for millimetre).
'divides' indicates putting letters inside.
'greek' becomes 'gr'.
'and' is a charade indicator (letters next to each other).
'arab' becomes 'ar' (abbreviation in Chambers).
'a'+'mm'='amm'
'gr'+'ar'='grar'
'amm' going inside 'grar' is 'GRAMMAR'.
(Other definitions for grammar that I've seen before include "Science of language" , "Study of basic linguistic units" , "Functions and relations of words in sentences" , "Basic rules of language" , "Correct usage of words" .)