Open-world object detection (OWOD) has recently obtained significant interest due to its practical applications. The core issue lies in a model’s ability to identify new object categories and incrementally acquire knowledge about them, all while retaining information about previously learned classes. Prior solutions have typically relied on either strong or weak supervision for the novel-class (i.e., out-of-distribution) data during detection, an approach that might not be applicable in real-world scenarios. This paper constructs a new setup where novel classes are only encountered on the fly at the inference stage. In response to this challenge, an innovative OWOD detector is tailored for the open-set incremental learning environment. The proposed methodology incorporates label smoothing as a mechanism to prevent the detector from prematurely and confidently assigning novel classes to existing categories, thereby facilitating the discovery of novel classes. Extensive experiments conducted on our realistic setup demonstrate the efficacy of our method for discovering novel classes in the new setup.