In any case, refusal may get up one's nose (5)
I believe the answer is:
annoy
'get up one's nose' is the definition.
'annoy' can be an answer for 'get' (thesaurus). I'm not certain of the 'up one's nose' bit.
'in any case refusal' is the wordplay.
'in' indicates putting letters inside.
'case refusal' becomes 'no' (I am not sure about this - if you are sure you should believe this answer much more).
'any' going around 'no' is 'ANNOY'.
'may' acts as a link.
Can you help me to learn more?
(Other definitions for annoy that I've seen before include "get angry" , "hack off" , "be a nuisance" , "Exasperate" , "Displease" .)