Abstract: Recent advances in speech language models have improved automatic speech recognition (ASR) for long-form audio. However, accurately and consistently transcribing domain-specific terminology remains challenging. Motivated by the world knowledge and contextual capability of large language models (LLMs), we propose Agentic-GER, an LLM-based agent for terminology correction in long-form speech. The agent uses global context from the full transcript to identify suspicious terms and resolve ambiguous hypotheses. It selectively re-transcribes the source speech to check candidate corrections, and uses accepted edits to guide subsequent decisions. Experiments with four LLMs and two ASR systems on GigaSpeechBench show consistent terminology improvements in both Chinese and English, with and without thinking. On Chinese speech, Agentic-GER achieves up to a 36.8% relative reduction in biased character error rate (B-CER) over the Whisper baseline.