By automating client engagement, fraudulent activities detection, compliance, credit evaluation, finance reports, and risk management processes, large language models (LLMs) can rapidly transform the banking industry. Nevertheless, there are considerable risks of cybersecurity and governance of LLMs in the context of financial institutions, such as insider threats, fast injection attacks, hallucinated financial responses, data leakage, and lack of compliance. AI systems that can ensure privacy, reliability, security, and integrity while meeting financial standards are critical components of banking systems. Focusing on runtime protection measures, access controls, and compliance policies, the article provides insight into cybersecurity governance frameworks for LLM financial systems. A framework for governance based on rapid validation, restriction of access, auditing, encryption, compliance monitoring, and human supervision is developed following the review of literature and analysis of risks faced. The results obtained during experiments reveal that cybersecurity governance frameworks help to mitigate risks associated with the application of artificial intelligence technologies while significantly improving operational security and compliance within the banking industry.