The register
The register lists The Fitzwilliam Hotel in Belfast as a licensed sponsor on Skilled Worker, an entry that goes back to at least 2026. Its rating on the register is Worker (A rating).
Fitzwilliam Hotel Limited is the registered name (Companies House number 04397168), a private limited company on the register since 2002. The registered office is at Mangham Works Mangham Road, Parkgate, Rotherham, South Yorkshire, S62 6EF, S62 6EF. By its SIC codes the business is in hospitality. It has traded under other names before, including Leasefocal Limited.
A licence says an organisation may sponsor; it does not say it is hiring today. The way to find out is the same as for any employer: the careers page, the job boards, and a direct approach with a UK-style CV that says early that sponsorship would be needed.