Quantum Machine Learning (QML) approaches introduce unique computational requirements that continuously emerge, from data encoding to model training, from data preparation to model deployment, thus spanning a wide range of possible scenarios. In contrast with classical machine learning, they require dynamic coordination of classical and quantum resources, such as the choice between real quantum processing units or simulators. Unfortunately, traditional MLOps frameworks, built around classical ML workflows, fail to accommodate this dynamic need for quantum resources throughout the pipeline. To address this limitation, we propose an MLOps framework that leverages cloud-native infrastructure, based on container orchestration, to support quantum-classical ML workflows, with dynamic allocation of quantum and classical resources, computational paradigm-agnostic orchestration, and flexible workflow management. These foundational factors unlock the potential of quantum machine learning through elastic hybrid architectures. Built on top of Kubernetes, our framework enables flexible allocation of quantum resources at any stage, without disrupting classical MLOps workflows and, consequently, ensuring traditional peculiarities, such as data and model versioning. This framework we design ensures consistent operations and fosters reproducibility across hybrid environments under a single infrastructure, hence providing a guiding framework for future-ready quantum-classical machine learning systems.