Bill for example’s taken first oath (4)
I believe the answer is:
egad
'oath' is the definition.
(archaic oath or exclamation)
'bill for example's taken first' is the wordplay.
'bill' becomes 'ad' (advertisement stuck on wall).
'for example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'taken first' means one lot of letters go next to another (some letters go before others).
'ad' after 'eg' is 'EGAD'.
(Other definitions for egad that I've seen before include "My word once" , "Oath sworn" , "Mild oath (archaic)" , "traditional oath" , "Christ" .)