Online recommenders have attained growing interest and created great revenue for businesses. Given numerous users and items, incremental update becomes a mainstream paradigm for learning large-scale models in industrial scenarios, where only newly arrived data within a sliding window is fed into the model, meeting the strict requirements of quick response. However, this strategy would be prone to overfitting to newly arrived data. When there exists a significant drift of data distribution, the long-term information would be discarded, which harms the recommendation performance. Conventional methods address this issue through native model-based continual learning methods, without analyzing the data characteristics for online recommenders. To address the aforementioned issue, we propose an incremental update framework for online recommenders with Data-Driven Prior (DDP), which is composed of Feature Prior (FP) and Model Prior (MP). The FP performs the click estimation for each specific value to enhance the stability of the training process. The MP incorporates previous model output into the current update while strictly following the Bayes rules, resulting in a theoretically provable prior for the robust update. In this way, both the FP and MP are well integrated into the unified framework, which is model-agnostic and can accommodate various advanced interaction models. Extensive experiments on two publicly available datasets as well as an industrial dataset demonstrate the superior performance of the proposed framework.