Yes, everyone’s right to work needs to be checked. Irish citizens were not required to apply under the EU Settlement Scheme and can live and work in the UK using their Irish passport or passport card (in either case, whether current or expired), or their Irish birth or adoption certificate together with an official document giving their National Insurance number and name.
Irish citizens can also apply for a frontier worker permit so they can prove their right to work using the Home Office online right to work service. A frontier worker is an EEA citizen who is resident outside the UK but who is economically active (employed or self-employed) in the UK.
