Vessel Traffic Services (VTS) are essential for maritime safety and regulatory compliance through real-time traffic management. However, with increasing traffic complexity and the prevalence of heterogeneous, multimodal data, existing VTS systems face limitations in spatiotemporal reasoning and intuitive human interaction. In this work, we propose VTS-LLM Agent, the first domain-adaptive large LLM agent tailored for interactive decision support in VTS operations. We formalize risk-prone vessel identification as a knowledge-augmented Text-to-SQL task, combining structured vessel databases with external maritime knowledge. To support this, we construct a curated benchmark dataset consisting of a custom schema, domain-specific corpus, and a query-SQL test set in multiple linguistic styles. Our framework incorporates NER-based relational reasoning, agent-based domain knowledge injection, semantic algebra intermediate representation, and query rethink mechanisms to enhance domain grounding and context-aware understanding. Experimental results show that VTS-LLM outperforms both general-purpose and SQL-focused baselines under command-style, operational-style, and formal natural language queries, respectively. Moreover, our analysis provides the first empirical evidence that linguistic style variation introduces systematic performance challenges in Text-to-SQL modeling. This work lays the foundation for natural language interfaces in vessel traffic services and opens new opportunities for proactive, LLM-driven maritime real-time traffic management.