The issue really will be with regulated service provision in the UK, if your business is resident in the EU, which may, or may not be subject to constraints.
Like Anna, I have clients pretty much all over the world, admittedly, most of these are law firms rather than directly the rights holder, but they are still non-EU businesses and I still take/give instruction from/to them and represent them here in Europe/France, and bill them accordingly. That has never been an issue.
So, for example, in my field of law, I will no longer be able to act in the for UK clients before the local intellectual property authorities, as I’m not licensed to practice in the UK. Currently, in the EU system, I can do this “occasionally” and could even have had my French qualifications recognised at the UK level should I so have chosen.
On the opposite side of the coin, take EU trademark representation for example. UK nationals will be excluded from representing any clients (irrespective of the client’s origin) before the EU community trademark office, unless they can show a mainland EU country national license to practice, or obtain an exemption, and also have a habitual place of business in one of the other 27 EU countries.
Post edit : I forgot to add that as a UK national, even if resident in one of the other 27 EU, I may be barred from carrying out certain reserved service activities in each particular state, depending on any recently drafted/implemented national law that deals with the rights of UK citizens after Brexit.