Deep learning-based malware classifiers face significant challenges due to concept drift. The rapid evolution of malware, especially with new families, can depress classification accuracy to near-random levels. Previous research has primarily focused on detecting drift samples, relying on expert-led analysis and labeling for model retraining. However, these methods often lack a comprehensive understanding of malware concepts and provide limited guidance for effective drift adaptation, leading to unstable detection performance and high human labeling costs. To address these limitations, we introduce DREAM, a novel system designed to surpass the capabilities of existing drift detectors and to establish an explanatory drift adaptation process. DREAM enhances drift detection through model sensitivity and data autonomy. The detector, trained in a semi-supervised approach, proactively captures malware behavior concepts through classifier feedback. During testing, it utilizes samples generated by the detector itself, eliminating reliance on extensive training data. For drift adaptation, DREAM enlarges human intervention, enabling revisions of malware labels and concept explanations embedded within the detector's latent space. To ensure a comprehensive response to concept drift, it facilitates a coordinated update process for both the classifier and the detector. Our evaluation shows that DREAM can effectively improve the drift detection accuracy and reduce the expert analysis effort in adaptation across different malware datasets and classifiers.