A transpace radio was a device for faster-than-light communications.
A spaceship constructed by the Voords had a room with a transpace radio. The First Doctor, who was being held prisoner by the Daleks on board, escaped and sent a transpace signal to Earth warning them that the Daleks and Voords were en route to the solar system. He was answered with a query regarding which planet the spaceship was heading for, but the Doctor did not know. (PROSE: Doctor Who and the Daleks)