... dim, initially boring, Shakespearean character (5)
I believe the answer is:
blear
'dim' is the definition.
(thesaurus)
'initially boring shakespearean character' is the wordplay.
'initially' suggests taking the first letters.
'shakespearean character' becomes 'lear'.
The first letter of 'boring' is 'b'.
'b'+'lear'='BLEAR'
(Other definitions for blear that I've seen before include "Baler (anag.)" , "Watery, blurred" , "Indistinct" , "Make (the eyes) dim" , "Blur" .)