Urge to proceed with Bill (4)
I believe the answer is:
goad
'urge' is the definition.
(thesaurus)
'proceed with bill' is the wordplay.
'proceed' becomes 'go' ('go' can be a synonym of 'proceed').
'with' is a charade indicator (letters next to each other).
'bill' becomes 'ad' (advertisement stuck on wall).
'go'+'ad'='GOAD'
'to' acts as a link.
(Other definitions for goad that I've seen before include "Spur, prod" , "Prompt" , "Spur, urge on" , "Arouse" , "Incite to act against one's inclination" .)