Such a conveyance is a vehicle carrying one in anger (8)
I believe the answer is:
carriage
'such a conveyance' is the definition.
(carriage is a kind of conveyance)
'vehicle carrying one in anger' is the wordplay.
'vehicle' becomes 'car' (car is a kind of vehicle).
'carrying' means one lot of letters go next to another (in a down clue, the bottom letters carry others).
'one' becomes 'i' (Roman numeral).
'in' is an insertion indicator.
'anger' becomes 'rage' (rage is a kind of anger).
'i' inserted within 'rage' is 'riage'.
'car'+'riage'='CARRIAGE'
'is a' is the link.
(Other definitions for carriage that I've seen before include "Engine- or horse-drawn vehicle" , "Vehicle - bearing" , "Conveyance (of items of merchandise)" , "Bearing, deportment" , "Perhaps a smoker's" .)