Proprietary large language models (LLMs) have been widely applied in various scenarios. Additionally, deploying LLMs on edge devices is trending for efficiency and privacy reasons. However, edge deployment of proprietary LLMs introduces new security challenges: edge-deployed models are exposed as white-box accessible to users, enabling adversaries to conduct effective model stealing (MS) attacks. Unfortunately, existing defense mechanisms fail to provide effective protection. Specifically, we identify four critical protection properties that existing methods fail to simultaneously satisfy: (1) maintaining protection after a model is physically copied; (2) authorizing model access at request level; (3) safeguarding runtime reverse engineering; (4) achieving high security with negligible runtime overhead. To address the above issues, we propose TransLinkGuard, a plug-and-play model protection approach against model stealing on edge devices. The core part of TransLinkGuard is a lightweight authorization module residing in a secure environment, e.g., TEE. The authorization module can freshly authorize each request based on its input. Extensive experiments show that TransLinkGuard achieves the same security protection as the black-box security guarantees with negligible overhead.