Suits worn by local for such a degree (4,4)
I believe the answer is:
fine arts
'such a degree' is the definition.
(Master of Fine Arts is an academic degree)
'suits worn by local' is the wordplay.
'suits' becomes 'fits' ('fit' can be a synonym of 'suit').
'worn by' means one lot of letters goes inside another (outside letters are worn by those on the inside).
'local' becomes 'near' (I've seen this in another clue).
'fits' enclosing 'near' is 'FINE ARTS'.
'for' acts as a link.
(Other definitions for fine arts that I've seen before include "Fan tries to get painting sculpture etc" , "Those appreciated for their beauty" , "Creative works appealing to sense of beauty" , "Aesthetic realm" , "culture" .)