<p>In our ever-evolving world, new data exhibits a long-tailed distribution, such as emerging images in varying amounts. This necessitates continuous model learning imbalanced data without forgetting, addressing the challenge of long-tailed class-incremental learning (LTCIL). Existing methods often rely on retraining linear classifiers with former data, which is impractical in real-world settings. In this paper, we harness the potent representation capabilities of pre-trained models and introduce AdaPtive Adapter RouTing (<span>Apart</span>) as an exemplar-free solution for LTCIL. To counteract forgetting, we train inserted adapters with frozen pre-trained weights for deeper adaptation and maintain a pool of adapters for selection during sequential model updates. Additionally, we present an auxiliary adapter pool designed for effective generalization, especially on minority classes. Adaptive instance routing across these pools captures crucial correlations, facilitating a comprehensive representation of all classes. Consequently, <span>Apart </span>tackles the imbalance problem as well as catastrophic forgetting in a unified framework. Extensive benchmark experiments validate the effectiveness of <span>Apart</span>.</p>