Enabling Large Language Models (LLMs) to evolve sustainably requires simultaneously preserving previously acquired knowledge (Past), effectively acquiring new task-specific skills (Present), and reserving sufficient parameter capacity for subsequent adaptation (Future). However, existing continual learning (CL) paradigms often prioritize immediate performance through dense updates, leading to catastrophic forgetting and rapid exhaustion of model capacity. To harmonize these conflicting demands, we draw inspiration from the brain’s functional partitioning and propose the Null-Space Constrained Parameter Region Specificity Method (PaRSP). PaRSP establishes a dynamic "Task-Region Mapping" that distinguishes between specialized neurons and generalist neurons. By precisely localizing a sparse "functional core" for each task, PaRSP restricts updates to specific regions via null-space orthogonality, preserving the vast majority of the network as an immutable "long-term memory bank." This induced sparsity not only enhances plasticity via targeted adaptation and minimizes interference to ensure stability, but also strategically reserves substantial capacity, securing sustainability for future evolution. Extensive experiments validate PaRSP’s state-of-the-art performance, particularly on Standard CL and Long Sequence benchmarks, effectively harmonizing the stability-plasticity-sustainability trade-off. Code is available at https://github.com/JinhuiBot/PaRSP