Pedestrian trajectory prediction is a critical component of intelligent transportation systems, supporting downstream tasks such as path planning and collision avoidance. Federated learning (FL) provides a decentralized alternative to centralized model training, enabling collaborative learning across clients without raw data sharing and thus improving data privacy. However, applying FL to trajectory prediction remains challenging due to behavioral variability across clients, model divergence, and instability under spatiotemporal heterogeneity. This paper introduces FedSTAR, a federated learning framework designed to improve prediction accuracy in such settings. FedSTAR integrates a two-stage contrastive alignment loss to enforce temporal consistency, an adaptive regularization mechanism to control local model drift, and a performance-aware aggregation strategy that prioritizes reliable client updates. Extensive experiments on the ETH and UCY datasets demonstrate that FedSTAR achieves consistently lower Average Displacement Error (ADE) and Final Displacement Error (FDE) than representative federated baselines across diverse non-IID and dynamic participation scenarios. These results indicate that FedSTAR enhances federated trajectory prediction accuracy under heterogeneous conditions while preserving data locality through decentralized training.