Education graduates quietly study cover at night (9)
I believe the answer is:
bedspread
'cover at night' is the definition.
(cover on a bed)
'education graduates quietly study' is the wordplay.
'education graduates' becomes 'BEds' (people with Bachelor of Education degrees).
'quietly' becomes 'p' (p for piano and quiet).
'study' becomes 'read' (synonyms).
'beds'+'p'+'read'='BEDSPREAD'
(Other definitions for bedspread that I've seen before include "Counterpane" , "Coverlet" , "Cover" .)