A degree Edward declined (6)
I believe the answer is:
abated
'declined' is the definition.
'a degree edward' is the wordplay.
'degree' becomes 'ba' (Bachelor of Arts).
'edward' becomes 'ted'.
'a'+'ba'+'ted'='ABATED'
(Other definitions for abated that I've seen before include "Decreased, receded" , "dropped off" , "Settled" , "Slackened off, died back" , "Slacked off, died away" .)