Continual Test-Time Adaptation (CTTA) aims to adapt a source pre-trained model to continually changing target domains during inference. As a fundamental principle, an ideal CTTA method should rapidly adapt to new domains (exploration) while retaining and exploiting knowledge from previously encountered domains to handle similar domains in the future. Despite significant advances, balancing exploration and exploitation in CTTA is still challenging: 1) Existing methods focus on adjusting predictions based on deep-layer outputs of neural networks. However, domain shifts typically affect shallow features, which are inefficient to be adjusted from deep predictions, leading to dilatory exploration; 2) A single model inevitably forgets knowledge of previous domains during the exploration, making it incapable of exploiting historical knowledge to handle similar future domains. To address these challenges, this paper proposes a mean teacher framework that strikes an appropriate Balance between Exploration and Exploitation (BEE) during the CTTA process. For the former challenge, we introduce a Multi-level Consistency Regularization (MCR) loss that aligns the intermediate features of the student and teacher models, accelerating adaptation to the current domain. For the latter challenge, we employ a Complementary Anchor Replay (CAR) mechanism to reuse historical checkpoints (anchors), recovering complementary knowledge for diverse domains. Experiments show that our method significantly outperforms state-of-the-art methods on several benchmarks, demonstrating its effectiveness for CTTA tasks.