State aid distributed by school centre (5)
I believe the answer is:
idaho
'state' is the definition.
(Idaho is an example)
'aid distributed by school centre' is the wordplay.
'distributed' indicates an anagram.
'by' is a charade indicator (letters next to each other).
'centre' says to take the centre.
The middle letters of 'school' are 'ho'.
'aid' is an anagram of 'ida'.
'ida'+'ho'='IDAHO'
(Other definitions for idaho that I've seen before include "US state, capital Boise" , "US state S. of Montana" , "One of 22 Across, capital Boise" , "somewhere in the US" , "US state in the Rocky Mountains" .)