Current and upcoming data-intensive Mission Critical (MC) applications rely on high Quality of Service (QoS) requirements related to connectivity, latency and network reliability. Beyond 5G networks shall accommodate MC services that enable voice, data and video transfer in extreme circumstances, for instance in occurrence of network overloads or infrastructure failures. In this work, we describe the specifications of the architectural framework that enables the roll-out of MC services over 5G networks and beyond, considering recent technological advancements of cloud-native functionalities, network slicing and edge deployments. The network architecture and the deployment process is described in three practical scenarios, including a capacity increase in the service load that necessitates the scaling of the computational resources, the deployment of a dedicated network slice for accommodating the stringent requirement of a MC application and a service migration scenario at the edge to cope with critical failures and QoS degradation. Furthermore, we illustrate the implementation of a Machine Learning (ML) algorithm that is used for overload prediction, validating its ability to predict the capacity increase and notify the components responsible to trigger the appropriate actions, based on a real dataset. To this end, we mathematically define the overload detection problem, as well as generalized prediction tasks in emergency situations and examine the key parameters (proactiveness ability, loockback window, etc.) of the ML model, also comparing its predictions abilities (~93% accuracy in overload detection) against multiple baseline classifiers. Finally, we demonstrate the flexibility of the ML model to achieve reliable predictions in scenarios with diverse requirements.