Recent research in brain tumor segmentation has shifted focus towards improving model adaptability through Domain-Incremental Learning (DIL). However, data heterogeneity across domains leads to catastrophic forgetting, and most replay-based methods are heavily reliant on the storage of original data. In this paper, we propose the Dynamic Replay-Driven Transformer (DRFormer) for Domain-Incremental Learning. Specifically, we introduce a strategy for dynamic feature replay, which eliminates the need for raw data storage by utilizing compressed domain representations extracted through a Global Encoder. Additionally, we design a Local Awareness Filtering Module (LAFM) to suppress domain-irrelevant features while aligning local correlations to reinforce domain-invariant representations. At the same time, we propose a Global Representation Calibration Module (GRCM), which refines global domain feature representations to ensure a more comprehensive and consistent knowledge retention process. Extensive experiments on four publicly available brain tumor MRI datasets demonstrate that DRFormer outperforms existing methods in both memory retention and generalization, offering a promising solution for domain-incremental medical image segmentation.