Stick no bill up (5)
I believe the answer is:
baton
'stick' is the definition.
(thesaurus)
'no bill up' is the wordplay.
'bill' becomes 'tab' (tab is a kind of bill**).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'no'+'tab'='notab'
'notab' reversed gives 'BATON'.
(Other definitions for baton that I've seen before include "Light wand" , "Relay race stick" , "Policeman's truncheon" , "Short stick" , "Short rod (that can be passed!)" .)