I'm familiar with the meaning "permission to be absent". It may be
extended to mean a chit, piece of paper, stating the permission to be
absent
OED:
exeat, v. and n.
Pronunciation: /??ksi?æt/
Etymology: Latin exeat let (him) go out, 3rd pers. singular present
subjunctive of exi-re to go out: see exit v. and n.
A. v. In Latin use as verb.
In plays of the early 16th c. used as a stage direction,
equivalent to the later exit v. and n.
a1556....
B. n. A permission to go out. [So used in French.]
1. A permission to leave the diocese, granted to a priest by the
bishop.
1730 N. Bailey et al. Dict. Britannicum, Exeat, (i.e. let him go
out) a term used in church-discipline for a permission, which a
bishop grants to a priest to go out of his diocese.
....
2. In English public schools and colleges, in monastic houses, etc.:
a permission for temporary absence.
1728 E. Chambers Cycl. (at cited word), His Master has given him
an Exeat.
1806 K. White Let. 30 June, He would not give me an exeat,
without which no man can leave his college for the night.
1852 C. A. Bristed Five Years Eng. University I. 193 (note) ,
Exeats..were never granted [at King's Coll. Camb.] but in cases of
life and death.
1859 F. W. Farrar Julian Home xx. 259 How shall I get my exeat
to go to London?
--
Peter Duncanson, UK
(in alt.usage.english)