Dictionary:

vicariate

  (vī-kâr'ē-ĭt, -āt', -kăr'-, vĭ-)

1. The office or authority of a vicar.
2. The district under a vicar's jurisdiction.

[Medieval Latin vicāriātus, from Latin vicārius, a substitute. See vicar.]

The noun has one meaning:

Meaning #1: the religious institution under the authority of a vicar
  Synonym: vicarship