is a monastery
governed by a prior or prioress. An alien priory is a priory which is dependent on a foreign mother house, and an alien priory cell was a residence of two or three monks dependent on a foreign mother house but sent to exploit a distant estate. Alien priory cells were suppressed in 1414.
The head of a priory is called a prior.
Strictly speaking a priory is a secondary house created by an existing abbey, but this distinction fell out of use in late mediaeval times.