Brief letter of refusal, extremely trite (4)
I believe the answer is:
note
'brief letter' is the definition.
(I've seen this before)
'refusal extremely trite' is the wordplay.
'refusal' becomes 'no'.
'extremely' means to remove the middle letters.
'trite' with its centre taken out is 'te'.
'no'+'te'='NOTE'
'of' is the link.
(Other definitions for note that I've seen before include "Single tone; short letter" , "Record; memo" , "Short written message" , "Memo; piano key" , "Mark - sound - money" .)