EURid, the governing body of the .eu regulatory framework - similar to ICANN for .com and CIRA for .ca - recently issued a policy update outlining the changes for UK citizens once Brexit comes into effect.
Read the full Brexit release here: https://eurid.eu/en/register-a-eu-domain/brexit-notice/
Moving forward, post the eventual Brexit event, EURid TLDs will be available to official residents that can demonstrate their locale as within the EU27 member states or their citizenship of the EU27 member states even if they reside outside the physical borders.
tl;dr If you are not located in the EU or an official citizen you will not be able to hold EURid governed TLDs such as .eu.
For existing UK residents or citizens, there will be a transition that may well see their domains revoked; there is no grandfathering. At the end of a probationary period - it appears EURid expects it to be 2 months - any EURid TLD that has not been updated to demonstrate the (presumably) UK-based domain holder as being a valid EUR27 citizen or location, per the above rules, their domain will be "Withdrawn"; in effect suspended.
The Withdrawn domains will sit (in purgatory) for 12 months after which they will be released for general registration again. It is unclear from the policy statement if a domain in Withdrawn status can be reclaimed legitimately by the original domain holder upon demonstrating eligibility.
If you currently hold a EURid domain such as .eu on one of its cyrillic variants, you will need to ensure you demonstrate EURid eligibility, ideally you get this completed before a Brexit event before any official changes start rolling out post-Brexit.