Edge-cloud systems, which bring computing, storage, and networking resources closer to end-users, offer significant advantages in reducing latency and enabling real-time data processing. Ensuring software reliability in these environments is critical, which has led to growing attention on Just-in-Time (JIT) defect prediction as an effective technique for prioritizing testing efforts by identifying code changes likely to introduce defects. However, edge-cloud systems often face challenges such as data scarcity, rapid project evolution, and limited historical defect information. These characteristics lead to the cold-start problem, where prediction models struggle to perform accurately on new or low-data projects due to the lack of training data. In this paper, we propose a novel prompt-based approach that uses Large Language Models (LLMs) in a prompt-based framework. By incorporating project evolution data directly into prompts, our approach enables LLMs to effectively capture the contextual information essential for accurate JIT defect prediction. Evaluation results demonstrate that our method significantly improves prediction performance, surpassing baseline method by an average of 13% in F1 score. This approach offers a practical solution for achieving high-accuracy JIT defect prediction in resource-constrained, rapidly evolving edge-cloud environments.