Sounds like education cut (6)
I believe the answer is:
lessen
'cut' is the definition.
(to cut can be to lessen)
'sounds like education' is the wordplay.
'sounds like' shows a homophone (sound like).
'education' becomes 'lesson' (lesson is a kind of education).
'lesson' is a homophone of 'LESSEN'.
(Other definitions for lessen that I've seen before include "Cut back or diminish" , "Abate" , "Make smaller for lenses" , "Decrease, diminish" , "Contract" .)