Theatre regularly left Bill filling horsey pantomime part (12)
I believe the answer is:
harlequinade
'pantomime part' is the definition.
(section of a pantomime)
'theatre regularly left bill filling horsey' is the wordplay.
'theatre regularly' becomes 'lrah' (I can't justify this - if you can you should believe this answer much more).
'left' says the letters should be written backwards.
'bill' becomes 'ad' (advertisement stuck on wall).
'filling' indicates putting letters inside.
'horsey' becomes 'equine' (I've seen this before).
'lrah' in reverse letter order is 'harl'.
'ad' inserted within 'equine' is 'equinade'.
'harl'+'equinade'='HARLEQUINADE'
(Other definitions for harlequinade that I've seen before include "Part of pantomime" , "Traditional pantomime episode" , "Pantomime; buffoonery" .)