Note everyone has bitterness (4)
I believe the answer is:
gall
'bitterness' is the definition.
(I know that bitterness can be written as gall)
'note everyone' is the wordplay.
'note' becomes 'g' (musical note).
'everyone' becomes 'all' (all people).
'g'+'all'='GALL'
'has' acts as a link.
(Other definitions for gall that I've seen before include "Effrontery" , "Irritate - presumption" , "This bladder is attached to the liver and stores bile" , "Bold impudent behaviour; abnormal growth on tree" , "Ill-will - bile" .)