How do UK companies remain GDPR compliant after Brexit?

UK companies remain compliant with GDPR after Brexit in exactly the same way as they remain compliant with GDPR before Brexit. Most companies who have been used to complying with the GDPR since it came into force in 2018, will just simply have to continue doing exactly the same thing. The only significant difference will be in the form of, if the company is holding data in respect of data subjects based in the EU and the company does not have an establishment in the EU then, as well as all of their other GDPR obligations that they are used to complying with, they will now have to appoint a representative in the EU as well.  That is unless there is an appropriate adequacy decision or some other mechanism agreed between the UK and the EU. The business will have to make sure that there are adequate safeguards in place for the transfer of data between the UK and the EU which will be international transfers after Brexit.