Whisper "need to run off" (9)
I believe the answer is:
undertone
'whisper' is the definition.
(thesaurus)
'need to run off' is the wordplay.
'off' indicates an anagram.
'need'+'to'+'run'='needtorun'
'needtorun' with letters rearranged gives 'UNDERTONE'.
(Other definitions for undertone that I've seen before include "Quiet way of speaking" , "Implicit meaning" , "Low or subdued voice pitch" .)