School papers centrally assessed by states (6)
I believe the answer is:
essays
'school papers' is the definition.
(I've seen this in another clue)
'centrally assessed by states' is the wordplay.
'centrally' means to look at the middle letters.
'by' means one lot of letters go next to another.
'states' becomes 'says' ('say' can be a synonym of 'state').
The middle of 'assessed' is 'es'.
'es'+'says'='ESSAYS'
(Other definitions for essays that I've seen before include "Students' works" , "Short pieces of writing on a particular subject" , "Tries to write compositions?" , "Tries for theses?" , "Attempts, writing" .)