A Hungarian independent court bailiff can only act in enforcement matters on the territory of Hungary (Vht. 232.§ (3)-(5). The independent court bailiff may not carry out enforcement actions outside the territory of Hungary, even if the proceedings were initiated in Hungary. If the claim affects or may affect assets in a European Union member state, it is possible to request the issuance of a European Enforcement Order so that the enforcement procedure can also be requested in EU member states with a document issued in Hungary for the assets found there.

You can read more about this at the following link: https://e-justice.europa.eu/54/HU/european_enforcement_order. It is also possible to start a European order for payment procedure, which you can read more about here:https://www.mokk.hu/ugyfeleknek/EUFMH.php.