Open-World Recognition (OWR) is an emerging study that constructs machine-learning models to recognize unknown classes and learn them continually. The classical formalization of OWR relies on three main components: classifier, unknown identification, and continual learning. However, fora model that operates on domain-specific tasks, training rejected unknown classes directly will harm the models in terms of effectivity and efficiency (i.e., a waste collector robot will learn unnecessary classes and will collect novel non-waste objects). Filtering these novel objects manually requires human-in-the-loop which is costly and unable to learn on the job. Therefore, in this study, we introduce and formalize Unsupervised Domain-specific Open-world Recognition (UDOR) that has the potential framework to achieve a fully automated agent in an open-world environment. In addition, we formalize the specific component in UDOR called novelty manager to assist the model to learn on the job. Furthermore, we propose a unified model using Continual Multi-Channel Contrastive Prototype Networks (CMCCPN), Automated Machine learning (AutoML), and class discovery with Hierarchical DBSCAN (HDBSCAN) or First Integer Neighbor Clustering Hierarchy (FINCH) as a step towards UDOR. Our experimentation results suggest that CMCCPN produced the highest performance, AutoML provides almost exemplary capability in differentiating novel classes, and Vision Transformer with HDBSCAN or FINCH shows a good technique to be investigated in discovering classes with a small number of classes. Our source code is available at https://github.com/gusti-alfarisy/udor.