Does a company in the UK need to appoint an EU representative after Brexit?

A business located in the UK that doesn’t have an establishment in the EU after Brexit and is regularly processing data on behalf of data subjects located in the EU, will in most circumstances have to appoint a representative after Brexit. There are some exemptions that apply but unless the business is capable of availing of some of the exemptions that are there then the business will need to appoint a representative in the EU, if it continues to process data of data subjects in the EU but doesn’t have its own establishment in the EU.