Federated learning-based Named Entity Recognition (FNER) has attracted widespread attention through decentralized training on local clients. However, most FNER models assume that entity types are pre-fixed, so in practical applications, local clients constantly receive new entity types without enough storage to access old entity types, resulting in severe forgetting on previously learned knowledge. In addition, new clients collecting only new entity types may join the global training of FNER irregularly, further exacerbating catastrophic forgetting. To overcome the above challenges, we propose a Forgetting-Subdued Learning (FSL) model which solves the forgetting problem on old entity types from both intra-client and inter-client two aspects. Specifically, for intra-client aspect, we propose a prototype-guided adaptive pseudo labeling and a prototypical relation distillation loss to surmount catastrophic forgetting of old entity types with semantic shift. Furthermore, for inter-client aspect, we propose a task transfer detector. It can identify the arrival of new entity types that are protected by privacy and store the latest old global model for relation distillation. Qualitative experiments have shown that our model has made significant improvements compared to several baseline methods.