Palmprint recognition is widely used in biometric systems, yet real-world performance often degrades due to feature distribution shifts caused by heterogeneous deployment conditions. Most deep palmprint models assume a closed and stationary distribution, leading to overfitting to dataset-specific textures rather than learning domain-invariant representations. Although data augmentation is commonly used to mitigate this issue, it assumes augmented samples can approximate the target deployment distribution, an assumption that often fails under significant domain mismatch. To address this limitation, we propose PalmBridge, a plug-and-play feature-space alignment framework for open-set palmprint verification based on vector quantization. Rather than relying solely on data-level augmentation, PalmBridge learns a compact set of representative vectors directly from training features. During enrollment and verification, each feature vector is mapped to its nearest representative vector under a minimum-distance criterion, and the mapped vector is then blended with the original vector. This design suppresses nuisance variation induced by domain shifts while retaining discriminative identity cues. The representative vectors are jointly optimized with the backbone network using task supervision, a feature-consistency objective, and an orthogonality regularization term to form a stable and well-structured shared embedding space. Furthermore, we analyze feature-to-representative mappings via assignment consistency and collision rate to assess model's sensitivity to blending weights. Experiments on multiple palmprint datasets and backbone architectures show that PalmBridge consistently reduces EER in intra-dataset open-set evaluation and improves cross-dataset generalization with negligible to modest runtime overhead.