High-efficiency Video Coding (HEVC) is a widely used video coding standard, and it has recently gained widespread adoption in various applications, such as video streaming, broadcasting, real-time conferencing, and storage. The adoption of Generative Adversarial Networks (GANs) into HEVC compression has shown significant improvements in compression performance by reducing the video size while maintaining the original quality. In this work, we explore the application of Knowledge Distillation to reduce the energy consumption associated with GAN-based HEVC. By training a smaller student model that imitates the larger teacher model's behavior, we significantly improved energy efficiency. In this paper, we provide a detailed study comparing the traditional HEVC algorithm, GAN-based HEVC, and GAN-based HEVC with Knowledge Distillation. The experimental results demonstrate a reduction in energy consumption of up to 30% while preserving video quality, making it an effective solution for video streaming platforms and energy-constrained devices and a sustainable solution for video compression without diminishing video quality.