To address the limitations of transductive learning in evolving real-world scenarios where unknown categories may continuously emerge, Continual Generalized Category Discovery (C-GCD) presents a novel paradigm that extends conventional category discovery frameworks. Unlike traditional static learning environments, C-GCD requires models to incrementally discover novel categories across multiple operational phases while maintaining discrimination capabilities for previously learned classes, posing significant challenges in balancing stability and plasticity. Prior approaches typically employ parameter-level knowledge distillation from historical models to alleviate catastrophic forgetting, which effectively preserves prior knowledge and optimizes computational efficiency. However, our analysis reveals that the persistent availability of samples from previous stages enables more sophisticated knowledge preservation strategies. Specifically, we present a Fix and Explore strategy that employs distinct learning methodologies for different types of potential data, aiming to preserve the features of old categories as much as possible and gradually exploring the potential distribution of new class latent spaces, we can enhance the model's ability to discover novel categories. This paper investigates this effect and introduces a novel heuristic paradigm to solve the C-GCD problem, called Fix and Explore (FaE), which aims to provide sufficient imaginative space for new classes while preserving the classification ability for old tasks. We conducted experiments across multiple datasets and performed detailed comparisons. The results demonstrate that our method achieves state-of-the-art performance at each stage across all datasets.