In real applications, person re-identification (ReID) is expected to retrieve the target person at any time, including both daytime and nighttime, ranging from short-term to long-term. However, existing ReID tasks and datasets can not meet this requirement, as they are constrained by available time and only provide training and evaluation for specific scenarios. Therefore, we investigate a new task called Anytime Person Re-identification (AT-ReID), which aims to achieve effective retrieval in multiple scenarios based on variations in time. To address the AT-ReID problem, we collect the first large-scale dataset, AT-USTC, which contains 403k images of individuals wearing multiple clothes captured by RGB and IR cameras. Our data collection spans 21 months, and 270 volunteers were photographed on average 29.1 times across different dates or scenes, 4-15 times more than current datasets, providing conditions for follow-up investigations in AT-ReID. Further, to tackle the new challenge of multi-scenario retrieval, we propose a unified model named Uni-AT, which comprises a multi-scenario ReID (MS-ReID) framework for scenario-specific features learning, a Mixture-of-Attribute-Experts (MoAE) module to alleviate inter-scenario interference, and a Hierarchical Dynamic Weighting (HDW) strategy to ensure balanced training across all scenarios. Extensive experiments show that our model leads to satisfactory results and exhibits excellent generalization to all scenarios.