Chaotic systems with extreme events present significant challenges in terms of prediction and control due to their complex nonlinear dynamics and potential high dimensionality. We investigate here the use of cluster-based reduced-order modelling (ROM) and control techniques applied to such systems. In this approach, we first model the dynamics of the system by identifying clusters of similar states and only model the transition between clusters. Then, based on those identified clusters, we define a per-cluster control parameter. This effectively neglects the specific dynamics within a given cluster while retaining the main dynamics of the full-order model. The considered test case is the Moehlis-Faisst-Eckhart (MFE) system which exhibits extreme events in the form of quasi-relaminarization events. The influence of the number of clusters and the order of modelling on the accuracy of the resulting reduced-order cluster-based model is explored. A cluster-based control strategy is also proposed and applied to the MFE system to prevent extreme events. This strategy manages to achieve the objectives with a large reduction in extreme events in the controlled MFE system, decreasing the amount of time spent in extreme state by 90% and the mean kinetic energy by 20%. This work highlights the potential of cluster-based reduced-order modelling and control.