Reading up Shakespeare is dull (4)
I believe the answer is:
drab
'dull' is the definition.
(synonyms)
'reading up shakespeare' is the wordplay.
'reading up' says the letters should be written backwards (in a down clue, letters go up).
'shakespeare' becomes 'bard' (I've seen this before).
'bard' back-to-front is 'DRAB'.
'is' acts as a link.
(Other definitions for drab that I've seen before include "woman with slatternly habits" , "Lacklustre" , "Dull sort of bard" , "Dingy - shabby" , "Dingy, dull" .)