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With the explosion of digital data in recent years, continuously learning new tasks from a stream of data without forgetting previously acquired knowledge has become increasingly important. In this paper, we propose a new continual learning (CL) setting, namely ``continual representation learning'', which focuses on learning better representation in a continuous way. We also provide two large-scale multi-step benchmarks for biometric identification, where the visual appearance of different classes are highly relevant. In contrast to requiring the model to recognize more learned classes, we aim to learn feature representation that can be better generalized to not only previously unseen images but also unseen classes/identities. For the new setting, we propose a novel approach that performs the knowledge distillation over a large number of identities by applying the neighbourhood selection and consistency relaxation strategies to improve scalability and flexibility of the continual learning model. We demonstrate that existing CL methods can improve the representation in the new setting, and our method achieves better results than the competitors.