Traffic prediction plays an important role in urban management. However, existing methods rely on centralized traffic data, which may raise privacy concerns. Federated traffic prediction offers a promising solution for clients (e.g., traffic management administrations) in different regions to collaboratively train models in a distributed manner without exposing private data. Nonetheless, data isolation inherently breaks the correlations between nodes (i.e., traffic sensors collecting data) from different regions, which leads to the missing inter-client dependency. Consequently, current works either fail to capture the missing inter-client dependency or compromise data privacy to recover the inter-client dependency. To address this issue, we propose a novel Federated method which recovers the inter-client dependency with HIdden global componeNTs (FedHINT). We find that the traffic data from different local regions actually contain hidden global components that reflect cross-regional traffic changes. Therefore, our FedHINT aims to extract hidden global components from each client to generate proxy nodes that represent global information, which are then utilized to recover the inter-client dependency. To be specific, we employ an attention module, which is guided by the shared global queries to capture hidden global components from local traffic data, to generate proxy nodes. Subsequently, our FedHINT adaptively learns the correlations between proxy nodes and local nodes through a global encoder. During this process, the global information in proxy nodes compensate for the loss of information from cross-regional nodes, which thereby recovers the missing inter-client dependency. Intensive experiments on multiple datasets demonstrate that our FedHINT significantly outperforms the state-of-the-art methods, with an average decrease of 3.73 and 4.81 on MAE and RMSE, respectively.