Real-time analytics and decision-making require online anomaly detection (OAD) to handle drifts in data streams efficiently and effectively. Unfortunately, existing approaches are often constrained by their limited detection capacity and slow adaptation to evolving data streams, inhibiting their efficacy and efficiency in handling concept drift, which is a major challenge in evolving data streams. In this paper, we introduce METER, a novel dynamic concept adaptation framework that introduces a new paradigm for OAD. METER addresses concept drift by first training a base detection model on historical data to capture recurring central concepts, and then learning to dynamically adapt to new concepts in data streams upon detecting concept drift. Particularly, METER employs a novel dynamic concept adaptation technique that leverages a hypernetwork to dynamically generate the parameter shift of the base detection model, providing a more effective and efficient solution than conventional retraining or fine-tuning approaches. Further, METER incorporates a lightweight drift detection controller, underpinned by evidential deep learning, to support robust and interpretable concept drift detection. We conduct an extensive experimental evaluation, and the results show that METER significantly outperforms existing OAD approaches in various application scenarios.