Artificial Intelligence (AI) and machine learning have seen significant growth in recent years, leading to an increased demand for computational resources. To meet this demand and to boost Europe’s competitive edge, the European Commission has built several supercomputers across the continent. However, these traditional supercomputers often lack modern APIs and automation tools necessary for AI development. This paper outlines how High-Performance Computing (HPC) systems and cloud platforms can be seamlessly integrated using ColonyOS, an open-source meta-operating system designed to connect and integrate diverse computing environments into a cohesive compute continuum. ColonyOS enables development of AI workflows that are portable across HPC systems and cloud environments, including Kubernetes, Docker, and Slurm. This integration makes it possible to develop automation workflows, such as training AI models on HPC systems and automatically deploy trained models to cloud platforms for inference. The paper details the architecture of ColonyOS and how it can be used to build AI applications that can run in an HPC-Cloud Continuum. This will be exemplified through a satellite image segmentation case study, showcasing the benefits of combining the Leonardo EuroHPC supercomputer with a Kubernetes cluster. Ultimately, ColonyOS paves the way for hyper-distributed AI applications that can seamlessly utilize both cloud and HPC systems, including existing EuroHPC supercomputers.