Motion sensor time-series are central to Human Activity Recognition (HAR), yet conventional approaches are constrained to fixed activity sets and typically require costly parameter retraining to adapt to new behaviors. While Large Language Models (LLMs) offer promising open-set reasoning capabilities, applying them directly to numerical time-series often leads to hallucinations and weak grounding. To address this challenge, we propose ZARA (Zero-training Activity Reasoning Agents), a knowledge- and retrieval-augmented agentic framework for motion time-series reasoning in a training-free inference setting. Rather than relying on black-box projections, ZARA distills reference data into a statistically grounded textual knowledge base that transforms implicit signal patterns into verifiable natural-language priors. Guided by retrieved evidence, ZARA iteratively selects discriminative cues and performs grounded reasoning over candidate activities. Extensive experiments on eight benchmarks show that ZARA generalizes robustly to unseen subjects and across datasets, demonstrating strong transferability across heterogeneous sensor domains. These results mark a step toward trustworthy, plug-and-play motion understanding beyond dataset-specific artifacts. Our code is available at https://github.com/zechenli03/ZARA.