Gait recognition aims to identify individuals at a distance based on their biometric gait patterns. While offering flexibility in network input, existing set-based methods often overlook the potential of fine-grained local feature by solely utilizing global gait feature and fail to fully exploit the communication between silhouette-level and set-level features. To alleviate this issue, we propose Gait Refined Lateral Network(GRLN), featuring plug-and-play Adaptive Feature Refinement modules (AFR) that extract discriminative features progressively from silhouette-level and set-level representations in a coarse-to-fine manner at various network depths. AFR can be widely applied in set-based gait recognition models to substantially enhance their gait recognition performance. To align with the extracted refined features, we introduce Horizontal Stable Mapping (HSM), a novel mapping technique that reduces model parameters while improving experimental results. To demonstrate the effectiveness of our method, we evaluate GRLN on two gait datasets, achieving the highest recognition rate among all set-based methods. Specifically, GRLN demonstrates an average improvement of 1.15% over the state-of-the-art set-based method on CASIA-B. Especially in the coat-wearing condition, GRLN exhibits a 5% improvement in performance compared to the contrast method GLN.