Priory was a set of companies set up in the 1970s by Mortimus under the alias "Robert Betram". For one of the companies Mortimus invented the CD a decade early to prevent the Seventh Doctor from hearing Plasticine's performance (which had originally been a bootleg cassette.) Priory also had access to a satellite in geostationary orbit called Skywatch. (PROSE: No Future)
Priory Records was another company, under whose label which Mortimus intended to release Plasticine's music. Following Mortimus' departure from Earth in 1976 the company went into liquidation. (PROSE: No Future)
The name "Priory" was likely chosen based on the title by which Mortimus was commonly known - a Priory is a haven for monks.