Announced a refusal to recognise (4)
I believe the answer is:
Here is my best explanation:
'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", "Have information", "Articulated", "Be aware of (something)", "Have awareness of", "Recognize", "Be familiar with", "Understand", "Recognise" and "Ken".)