"hired a gig from the ostler at the Duke of Cumberland Hotel"
The Duke of Cumberland, Whitstable
Creative Commons AttributionThe Duke of Cumberland, Whitstable - Credit: stavros1, Wikimedia Commons

A gig, sometimes known as a chaise, a chair or a trap, is a light two-wheeled carriage drawn by one horse. Click here to see a picture.

An ostler looked after the horses and stables at an inn.

The Duke of Cumberland is a hotel and public house on Whitstable High Street. At one time it was a popular drinking venue for the local oyster dredgers. It dates back to the late 16th Century and was originally known as The Noah's Ark, but the name was changed to commemorate Prince William, Duke of Cumberland putting down the Jacobite Rising at the Battle of Culloden in 1746.