Final answer:
A covered passage between the transept and chapter house of a cathedral is known as a cloister.
Step-by-step explanation:
The covered passage, especially one between the transept and chapter house of a cathedral, is known as a cloister. The cloister is a typically arcaded area providing a place of quiet and reflection for the clergy, sometimes leading to other parts of the religious complex such as the chapter house. This architectural feature is commonplace in Gothic and Romanesque church designs, which emphasizes the functionality of managing the flow of traffic and providing solitude for meditation and peaceful ambulation within the church grounds.