The Supreme Court of the UK resumes hearing cases at the start of Michaelmas Term which commences on 2 October 2023 - Judicial Sittings 2023 Michaelmas Term - The Supreme Court.
Of the appeals to be heard, it will be the government's appeal relating to the Rwanda policy that come to political and public attention. The appeal will be heard from 9 to 11 October.
The Court of Appeal (Civil Division) judgment was handed down in April 2023 - Law and Lawyers: A note on AAA v Secretary of State for the Home Department ~ removals to Rwanda (obiterj.blogspot.com)
The legal questions to be decided by the Supreme Court are set out at R (on the application of AAA and others) (Respondents/Cross Appellants) v Secretary of State for the Home Department (Appellant/Cross Respondent) - The Supreme Court
The court's constitution is to be Lord Reed (President), Lord Hodge (Deputy President), Lord Lloyd-Jones, Lord Briggs and Lord Sales. By October, those will be the five most senior Justices.
Currently the court has only one female member - Lady Rose. As Joshua Rozenberg notes - Justices named for Rwanda appeal - by Joshua Rozenberg (substack.com) - that is likely to change in the near future.