The Collaborative International Dictionary
Arches \Arch"es\, pl. of Arch, n.
Court of arches, or Arches Court (Eng. Law), the court of
appeal of the Archbishop of Canterbury, whereof the judge,
who sits as deputy to the archbishop, is called the Dean
of the Arches, because he anciently held his court in the
church of St. Mary-le-Bow (de arcubus). It is now held in
Westminster.
--Mozley & W.
Wikipedia
The Arches Court, presided over by the Dean of Arches, is an ecclesiastical court of the Church of England covering the Province of Canterbury. Its equivalent in the Province of York is the Chancery Court.
Usage examples of "arches court".
There were a great many bundles of papers on it, some endorsed as Allegations, and some (to my surprise) as Libels, and some as being in the Consistory Court, and some in the Arches Court, and some in the Prerogative Court, and some in the Admiralty Court, and some in the Delegates' Court.