The EU AI Act (AIA) mandates the implementation of a risk management system (RMS) and a quality management system (QMS) for high-risk AI systems. The ISO/IEC 42001 standard provides a foundation for fulfilling these requirements but does not cover all EU-specific regulatory stipulations. To enhance the implementation of the AIA in Germany, the Federal Office for Information Security (BSI) could introduce the national standard BSI 200-5, which specifies AIA requirements and integrates existing ISMS standards, such as ISO/IEC 27001. This paper examines the interfaces between an information security management system (ISMS) and an AI management system (AIMS), demonstrating that incorporating existing ISMS controls with specific AI extensions presents an effective strategy for complying with Article 15 of the AIA. Four new AI modules are introduced, proposed for inclusion in the BSI IT Grundschutz framework to comprehensively ensure the security of AI systems. Additionally, an approach for adapting BSI's qualification and certification systems is outlined to ensure that expertise in secure AI handling is continuously developed. Finally, the paper discusses how the BSI could bridge international standards and the specific requirements of the AIA through the nationalization of ISO/IEC 42001, creating synergies and bolstering the competitiveness of the German AI landscape.