In next-generation 6G scenarios, non-terrestrial net-works employing low Earth orbit (LEO) satellites will be pivotal in achieving ultra-wide coverage, ultra-connectivity, and ultra-precision. Although LEO satellites provide comprehensive global coverage, their rapid mobility introduces frequent handovers, requiring sophisticated scheduling to maintain uninterrupted service. This paper proposes a deep reinforcement learning-based scheduling algorithm in order to improve service rate and continuity for terrestrial users in multi-LEO) environments.