You asked
I would like information regarding the appointment process for being on the ONS board.
We said
Thank you for your request.
The Office for National Statistics (ONS) is the executive office of the UK Statistics Authority (UKSA). Although the ONS does not have a Board, the UKSA does. Appointments are made via open competition, however, we have no responsibility for this process, nor any records about how it has been completed. This is the responsibility of the Cabinet Office public appointments team whose contact details can can be found at the following link.
https://publicappointments.cabinetoffice.gov.uk/contact-us/
For the purposes of your research you my find the following link to the UK Statistics Authority homepage useful; https://www.statisticsauthority.gov.uk/about-the-authority/meet-the-board/
Page 17 of the report in the following link may also be of interest to you; https://publicappointmentscommissioner.independent.gov.uk/wp-content/uploads/2018/10/Annual-Report-17-18-2.pdf