Autonomous navigation in real-world environments often requires long-horizon operation under partial observability and evolving goals. Existing mapless navigation approaches predominantly assume fixed goals throughout an episode, limiting applicability to practical scenarios where goals change online during execution. We study online chained-goal navigation, where goals evolve through existing-goal redirection or new-goal emergence without explicit transition signals. Under this setting, we find navigation may require either continued exploration or strategic revisitation, creating conflicting memory requirements. We propose Global-Local Spatio-Temporal Belief Learning (GLST), a memory-decomposition framework that separates latent beliefs into global-local spatial and long-short temporal representations for long-horizon reasoning. We further introduce goal-conditioned rewards to balance exploration and exploitation under evolving goals. Extensive experiments in simulation across diverse terrains demonstrate improved chained-goal navigation performance over baselines. Real-robot experiments using the Spot quadruped further validate our memory decomposition framework.

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