Carters did not have to be licenced by a Society, if they had to be licenced at all it would be by the Police, or the local authority.
It all depends on what you mean by a 'carter'? He was not necessarily some one who drove what is normally known a cart, it could be any wheeled vehicle, but a cart, wagon, dray etc. are specific types of vehicle.
The usual term in country districts was a Carter, or a Carrier if he conveyed passengers.
There was also a Carman who drove a horse drawn vehicle, usually in towns, collecting and delivering goods. A Bonded Carman was employed by a cartage contractor in conveying dutiable goods from/to a bonded warehouse.
The Carmen's Company is a guild of the City of London, reflecting the transport industry in all its modes, but particularly surface transport - road and rail, goods and passenger.
See
http://www.thecarmen.co.uk/companytoday/whoare.shtmlStan