Any financial institution established and regulated in another EU member state must notify the regulator of the member state in which the company intends to do business of that intention. It's called 'freedom to provide services' that is, if the company does not have a physical base in the target member state . If the company intends to set up a branch/office other than a head office, it's called 'freedom of establishment' .
Either way, the regulator should be informed.