County school's first charter (5)
I believe the answer is:
shire
'county' is the definition.
(thesaurus)
'school's first charter' is the wordplay.
'first' suggests taking the first letters.
'charter' becomes 'hire' ('hire' can be a synonym of 'charter').
The first letter of 'schools' is 's'.
's'+'hire'='SHIRE'
(Other definitions for shire that I've seen before include "Rural county" , "Heavy horse" , "Breed of draught horse" , "Powerful draught horse" , "Berks" .)