Encouraged to be terribly rude with note (5)
I believe the answer is:
urged
'encouraged' is the definition.
(I've seen this before)
'terribly rude with note' is the wordplay.
'terribly' indicates an anagram.
'with' is an insertion indicator.
'note' becomes 'g' (musical note).
'rude' is an anagram of 'ured'.
'ured' enclosing 'g' is 'URGED'.
'to be' acts as a link.
(Other definitions for urged that I've seen before include "Egged on" , "Incited" , "Beseeched" , "Impelled - encouraged" , "Exhorted or prodded" .)