Effective management and operational decision-making for complex mobile network systems present significant challenges, particularly when addressing conflicting requirements such as efficiency, user satisfaction, and energy-efficient traffic steering. The literature presents various approaches aimed at enhancing network management, including the Zero-Touch Network (ZTN) and Self-Organizing Network (SON); however, these approaches often lack a practical and scalable mechanism to consider human sustainability goals as input, translate them into energy-aware operational policies, and enforce them at runtime. In this study, we address this gap by proposing the AGORA: Agentic Green Orchestration Architecture for Beyond 5G Networks. AGORA embeds a local tool-augmented Large Language Model (LLM) agent in the mobile network control loop to translate natural-language sustainability goals into telemetry-grounded actions, actuating the User Plane Function (UPF) to perform energy-aware traffic steering. The findings indicate a strong latency-energy coupling in tool-driven control loops and demonstrate that compact models can achieve a low energy footprint while still facilitating correct policy execution, including non-zero migration behavior under stressed Multi-access Edge Computing (MEC) conditions. Our approach paves the way for sustainability-first, intent-driven network operations that align human objectives with executable orchestration in Beyond-5G infrastructures.