Lifelong Person Re-identification (L-ReID) aims to learn from sequentially collected data to match a person across different scenes. Once an L-ReID model is updated using new data, all historical images in the gallery are required to be re-calculated to obtain new features for testing, known as ``re-indexing''. However, it is infeasible when raw images in the gallery are unavailable due to data privacy concerns, resulting in incompatible retrieval between the query and the gallery features calculated by different models, which causes significant performance degradation. In this paper, we focus on a new task called Re-indexing Free Lifelong Person Re-identification (RFL-ReID), which requires achieving effective L-ReID without re-indexing raw images in the gallery. To this end, we propose a Continual Compatible Representation (C2R) method, which facilitates the query feature calculated by the continuously updated model to effectively retrieve the gallery feature calculated by the old model in a compatible manner. Specifically, we design a Continual Compatible Transfer (CCT) network to continuously transfer and consolidate the old gallery feature into the new feature space. Besides, a Balanced Compatible Distillation module is introduced to achieve compatibility by aligning the transferred feature space with the new feature space. Finally, a Balanced Anti-forgetting Distillation module is proposed to eliminate the accumulated forgetting of old knowledge during the continual compatible transfer. Extensive experiments on several benchmark L-ReID datasets demonstrate the effectiveness of our method against state-of-the-art methods for both RFL-ReID and L-ReID tasks. The source code of this paper is available at https://github.com/PKU-ICST-MIPL/C2R_CVPR2024.