The register
The register lists Leiths (Scotland) Ltd in Aberdeen as a licensed sponsor on Skilled Worker, an entry that goes back to at least 2026. Rating on the current register: Worker (A rating).
Leiths (scotland) Limited is the registered name (Companies House number SC062692), a private limited company on the register since 1977. Registered office: Rigifa, Cove, Aberdeen, AB12 3LR, AB12 3LR. Its filed activity puts it in mining and quarrying. It has traded under other names before, including Leith's Transport (aberdeen) 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.