Announced a refusal to recognise (4)
I believe the answer is:
know
'recognise' is the definition.
('know' can be a synonym of 'recognize')
'announced a refusal' is the wordplay.
'announced' shows a homophone (sound like).
'a refusal' becomes 'no'.
'no' sounds like 'KNOW'.
'to' acts as a link.
(Other definitions for know that I've seen before include "A Channel port, type of sole" , "Recognise" , "Articulated" , "Be aware of (something)" , "Understand" .)