Mounting rubbish delivered that swamps City boss (8)
I believe the answer is:
director
'boss' is the definition.
(I know that boss can be written as director)
'mounting rubbish delivered that swamps city' is the wordplay.
I cannot really understand how this works, but
'city' could be 'ec' (the City of London postcode) and 'ec' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for director that I've seen before include "One who controls resources and expenditures" , "Controller of production or member of a board" , "Business manager or film maker" , "Creditor (anag.)" , "Company board member" .)