Island school, one on a detached part of Italy (6)
I believe the answer is:
ischia
'detached part of italy' is the definition.
(Italian island)
'island school one on a' is the wordplay.
'island' becomes 'i' (geographical abbreviation).
'school' becomes 'sch' (common abbreviation).
'one' becomes 'i' (Roman numeral).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'i'+'sch'+'i'+'a'='ISCHIA'
(Other definitions for ischia that I've seen before include "Volcanic island in the Tyrrhenian Sea" , "Heavily populated island in the Gulf of Naples" , "Home of islander" , "Volcanic island in the Bay of Naples" , "bits of hipbone" .)