Old man ignoring final bill? Idiot! (7)
I believe the answer is:
fathead
'idiot' is the definition.
(fathead can mean a foolish person)
'old man ignoring final bill?' is the wordplay.
'old man' becomes 'father' (I've seen this before).
'ignoring final' means to remove the last letter (the final letter is ignored).
'bill?' becomes 'ad' (advertisement stuck on wall).
'father' with its last letter taken off is 'fathe'.
'fathe'+'ad'='FATHEAD'
(Other definitions for fathead that I've seen before include "Slang idiot with enlarged cranium?" , "silly ass!" , "Stupid person" , "Dimwit" , "Charlie" .)