The Department of Culture Media and Sport has issued two separate sets of guidance covering the NIS Directive and .eu domain names registered by UK entities should the UK leave the EU without a deal.
The NIS Guidance confirms that the Directive will continue to apply after we leave the EU but highlights that any relevant digital service provider (RDSP) may need to appoint a representative in an EU member state should they wish to continue to offer services to the EU after the 29th of March. Where such a representative is appointed, the RDSP will be under the jurisdiction of that EU Member State.
The guidance on .eu top level domain names confirms that entities and individuals that are established or reside in the UK will no longer be eligible to register .eu domain names or be able to renew them before the withdrawal date. The Commission’s notice on the issues also states that the Registry will be entitled to revoke a domain name where the holder no longer meets the eligibility criteria (which is probably the case once the UK has left) on its own initiative so any .eu websites and email addresses may become inaccessible
You can read the NIS guidance in full here and the .eu domain name guidance here.