Leith was a port close to Edinburgh. It was located somewhere beyond the town walls.
When Bill Potts questioned whether the Twelfth Doctor was sure that they had landed in Edinburgh, commenting "It's a little bit grimmer than it looks on telly", the Doctor replied "It's probably just Leith". Later a soldier pointed at Bill and commented "Looks Barbary to me. Must hae come off a ship in Leith". Regarding the plague, Agnes stated that if they hadn't closed the gates, they would have had half of Leith bringing it into the town. (PROSE: Plague City)