Continual learning (CL) addresses the problem of catastrophic forgetting in neural networks, which occurs when a trained model tends to overwrite previously learned information, when presented with a new task. CL aims to instill the lifelong learning characteristic of humans in intelligent systems, making them capable of learning continuously while retaining what was already learned. Current CL problems involve either learning new domains (domain-incremental) or new and previously unseen classes (class-incremental). However, general learning processes are not just limited to learning information, but also refinement of existing information. In this paper, we define CLEO -- Continual Learning of Evolving Ontologies, as a new incremental learning setting under CL to tackle evolving classes. CLEO is motivated by the need for intelligent systems to adapt to real-world ontologies that change over time, such as those in autonomous driving. We use Cityscapes, PASCAL VOC, and Mapillary Vistas to define the task settings and demonstrate the applicability of CLEO. We highlight the shortcomings of existing CIL methods in adapting to CLEO and propose a baseline solution, called Modelling Ontologies (MoOn). CLEO is a promising new approach to CL that addresses the challenge of evolving ontologies in real-world applications. MoOn surpasses previous CL approaches in the context of CLEO.