A refusal, in any case, will displease (5)
I believe the answer is:
annoy
'displease' is the definition.
(I know that annoy is a kind of displease)
'a refusal in any' is the wordplay.
'a refusal' becomes 'no' (it's a no).
'in' indicates putting letters inside.
'no' placed inside 'any' is 'ANNOY'.
'case will' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for annoy that I've seen before include "Upset" , "get angry" , "Nark - nettle" , "Displease" , "Irritate, nettle" .)