Quickly send: has note (9)
I believe the answer is:
posthaste
'quickly' is the definition.
(thesaurus)
'send has note' is the wordplay.
'send' becomes 'post' ('post' can be a synonym of 'send').
'note' becomes 'te' (**).
'post'+'has'+'te'='POSTHASTE'
(Other definitions for posthaste that I've seen before include "With great speed and urgency" , "Quick" , "Hurry the mail with utmost speed" , "With great speed, after hurry" , "With great speed, like delivery of letters?" .)