This paper explores automated support for test maintenance (adding, removing, or modifying test cases), which is a costly and laborious task in the software testing process. In particular, we investigate how to support test maintenance by leveraging large-scale language models (LLMs) through a case study at Ericsson AB. We analyze the LLM to predict when test maintenance is needed, what tasks it can perform, and what to consider when deploying it in an industrial environment, and propose and demonstrate a multi-agent architecture that predicts which tests will require maintenance after source code changes. In conclusion, this study enhances theoretical and practical understanding of how to apply LLMs to test maintenance processes in industrial settings.