This is how we do it in the UK.
For Supreme Court justices the selection process is slightly different in that the Minister of Justice convenes the selection panel (constitution is defined in law)
1.the President of the UKSC, who will be the chair of the selection commission; 2.a senior UK judge (who is not a UKSC Justice) nominated by the President of the UKSC; 3.a member of the Judicial Appointments Commission for England & Wales; 4.a member of the Judicial Appointments Board for Scotland; and 5.a member of the Northern Ireland Judicial Appointments Commission.
Members of the JAC are senior civil servants and by law must remain politically neutral.