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In real-world applications, the process generating the data might suffer from nonstationary effects (e.g., due to seasonality, faults affecting sensors or actuators, and changes in the users' behaviour). These changes, often called concept drift, might induce severe (potentially catastrophic) impacts on trained learning models that become obsolete over time, and inadequate to solve the task at hand. Learning in presence of concept drift aims at designing machine and deep learning models that are able to track and adapt to concept drift. Typically, techniques to handle concept drift are either active or passive, and traditionally, these have been considered to be mutually exclusive. Active techniques use an explicit drift detection mechanism, and re-train the learning algorithm when concept drift is detected. Passive techniques use an implicit method to deal with drift, and continually update the model using incremental learning. Differently from what present in the literature, we propose a hybrid alternative which merges the two approaches, hence, leveraging on their advantages. The proposed method called Hybrid-Adaptive REBAlancing (HAREBA) significantly outperforms strong baselines and state-of-the-art methods in terms of learning quality and speed; we experiment how it is effective under severe class imbalance levels too.