Dull, a degree dry (4)
I believe the answer is:
matt
'dull' is the definition.
('matt' can be similar in meaning to 'dull')
'a degree dry' is the wordplay.
'a degree' becomes 'ma' (Master of Arts is a type of degree**).
'dry' becomes 'tt' (abbreviation for teetotal).
'ma'+'tt'='MATT'
(Other definitions for matt that I've seen before include "Dull uniform finish" , "book" , "(Of surface) dull" , "Without a shine, dull" , "Telegraph cartoonist" .)