Federated Learning (FL) enables collaborative model training across distributed clients without sharing raw data, offering a significant privacy benefit. However, most existing Personalized Federated Learning (pFL) methods assume a static client participation, which does not reflect real-world scenarios where new clients may continuously join the federated system (i.e., dynamic client onboarding). In this paper, we explore a practical scenario in which a new batch of clients is introduced incrementally while the learning task remains unchanged. This dynamic environment poses various challenges, including preserving performance for existing clients without retraining and enabling efficient knowledge transfer between client batches. To address these issues, we propose Personalized Federated Data-Free Sub-Hypernetwork (pFedDSH), a novel framework based on a central hypernetwork that generates personalized models for each client via embedding vectors. To maintain knowledge stability for existing clients, pFedDSH incorporates batch-specific masks, which activate subsets of neurons to preserve knowledge. Furthermore, we introduce a data-free replay strategy motivated by DeepInversion to facilitate backward transfer, enhancing existing clients' performance without compromising privacy. Extensive experiments conducted on CIFAR-10, CIFAR-100, and Tiny-ImageNet demonstrate that pFedDSH outperforms the state-of-the-art pFL and Federated Continual Learning baselines in our investigation scenario. Our approach achieves robust performance stability for existing clients, as well as adaptation for new clients and efficient utilization of neural resources.