In recent years, there has been remarkable progress in the field of digital pathology, driven by the ability to model complex tissue patterns using advanced deep-learning algorithms. However, the robustness of these models is often severely compromised in the presence of data shifts (e.g., different stains, organs, centers, etc.). Alternatively, continual learning (CL) techniques aim to reduce the forgetting of past data when learning new data with distributional shift conditions. Specifically, rehearsal-based CL techniques, which store some past data in a buffer and then replay it with new data, have proven effective in medical image analysis tasks. However, privacy concerns arise as these approaches store past data, prompting the development of our novel Generative Latent Replay-based CL (GLRCL) approach. GLRCL captures the previous distribution through Gaussian Mixture Models instead of storing past samples, which are then utilized to generate features and perform latent replay with new data. We systematically evaluate our proposed framework under different shift conditions in histopathology data, including stain and organ shift. Our approach significantly outperforms popular buffer-free CL approaches and performs similarly to rehearsal-based CL approaches that require large buffers causing serious privacy violations.