UK citizens are not considered to be ‘non-nationals’ for the purposes of Irish immigration law. They continue to enjoy arrangements under the Common Travel Area (CTA) including the freedom to reside in the State following the UK's departure from the European Union on 31 December 2020.
UK nationals do not require any documentation to continue their lives in Ireland after that date, but may request a Withdrawal Agreement Beneficiary Card under the Withdrawal Agreement, if they so wish. This card is free of charge and can be obtained by making an application on my Department’s online registration renewal system at: inisonline.jahs.ie/user/login .
More information is available on my Department's website at:
www.irishimmigration.ie/extension-of-date-for-non-eea-family-members-of-uk-nationals-residing-in-ireland-before-the-end-of-the-transition-period-on-31-december-2020-to-apply-for-a-residence-document-under-the-withdrawal-agre/
As their residency in the State is secured, they would not be considered to be undocumented and, consequently, are not eligible to apply for the Regularisation Scheme.
It should also be noted that any person born outside of Ireland to Irish parents may be entitled to Irish citizenship, on registering the birth with the Department of Foreign Affairs. Further details are available at:
www.irishimmigration.ie/how-to-become-a-citizen/check-if-you-are-an-irish-citizen-by-birth-or-descent/