Edward promises to be dull (7)
I believe the answer is:
tedious
'be dull' is the definition.
(similar in meaning)
'edward promises' is the wordplay.
'edward' becomes 'ted'.
'promises' becomes 'IOUs' (promises to pay a debt).
'ted'+'ious'='TEDIOUS'
'to' is the link.
(Other definitions for tedious that I've seen before include "Wearisome, boring" , "drab" , "awfully boring" , "Boring, monotonous" , "flat" .)