At European level, so far there has been no harmonised set of rules governing the market access for third-country undertakings that intend to conduct banking activities in the EU. Although, after Brexit, European supervisory authorities have promulgated their supervisory expectations with regard to third-country undertakings that have established bank subsidiaries in the EU, there has been no binding framework that applies uniformly in all EU Member States and, thus, prevents regulatory arbitrage. In particular, there have been no harmonised binding rules for access to the EU market through third-country banking branches and on a cross-border basis. With the introduction of CRD 6, an attempt is now being made to close this legal gap. This article provides an overview of the future legal framework and the potential impact on the business models of third-country undertakings with a particular focus on third-country branches.