The Collaborative International Dictionary of English v.0.48:

Exeat \Ex"e*at\, n. [L., let him go forth.]
   1. A license for absence from a college or a religious house.
      [Eng.] --Shipley.
      [1913 Webster]

   2. A permission which a bishop grants to a priest to go out
      of his diocese. --Wharton.
      [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

EXEAT, eccl. law. This is a Latin term, which is used to express the written
permission which a bishop gives to an ecclesiastic to exercise the functions
of his ministry in another diocese.