Quick study after sending us note (6)
I believe the answer is:
sudden
'quick' is the definition.
(similar in meaning)
'study after sending us note' is the wordplay.
'study' becomes 'den' (den can mean an office or study).
'after' is a charade indicator (letters next to each other).
'sending' is an anagram indicator (letters are sent to different positions).
'note' becomes 'D' (musical note).
'us' anagrammed gives 'su'.
'su'+'d'='sud'
'den' put after 'sud' is 'SUDDEN'.
(Other definitions for sudden that I've seen before include "Occurring quickly without warning" , "Happening abruptly" , "Rapid and unexpected" , "Done unexpectedly" , "Swift" .)