Vision-based 3D semantic occupancy prediction is vital for autonomous driving, enabling unified modeling of static infrastructure and dynamic agents. Global occupancy maps serve as long-term memory priors, providing valuable historical context that enhances local perception. This is particularly important in challenging scenarios such as occlusion or poor illumination, where current and nearby observations may be unreliable or incomplete. Priors aggregated from previous traversals under better conditions help fill gaps and enhance the robustness of local 3D occupancy prediction. In this paper, we propose Long-term Memory Prior Occupancy (LMPOcc), a plug-and-play framework that incorporates global occupancy priors to boost local prediction and simultaneously updates global maps with new observations. To realize the information gain from global priors, we design an efficient and lightweight Current-Prior Fusion module that adaptively integrates prior and current features. Meanwhile, we introduce a model-agnostic prior format to enable continual updating of global occupancy and ensure compatibility across diverse prediction baselines. LMPOcc achieves state-of-the-art local occupancy prediction performance validated on the Occ3D-nuScenes benchmark, especially on static semantic categories. Furthermore, we verify LMPOcc's capability to build large-scale global occupancy maps through multi-vehicle crowdsourcing, and utilize occupancy-derived dense depth to support the construction of 3D open-vocabulary maps. Our method opens up a new paradigm for continuous global information updating and storage, paving the way towards more comprehensive and scalable scene understanding in large outdoor environments.