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 subsidiary indication.
'announced' indicates a 'sounds like' (homophone) clue.
'a refusal' becomes 'no'.
'no' is a homophone of 'know'.
'to' is the link.
(Other definitions for know that I've seen before include "A Channel port, type of sole", "Realise", "Have information", "Understand", "Be familiar with", "Have awareness of", "Be aware of (something)", "Recognize", "Recognise" and "Be sure of something".)