Corporation anger reduced after introduction of British vehicle (7)
I believe the answer is:
tumbril
'vehicle' is the definition.
(tumbril is a kind of vehicle)
'corporation anger reduced after introduction of british' is the wordplay.
I cannot really understand how this works, but
'corporation' could be 'tum' (I've seen this in other clues) and 'tum' is present in the answer.
'british' could be 'br' and 'br' is present in the answer.
This explanation may well be incorrect...
(Other definitions for tumbril that I've seen before include "Conveyance to the guillotine" , "Revolutionary transport" , "Transport to the guillotine; limb rut (anag.)" , "Cart that carried prisoners to the guillotine" , "Transport to guillotine; Mr built (anag.)" .)