This paper introduces a novel approach using deep reinforcement learning (DRL) to enhance network slicing planning and handovers in satellite networks. We propose a proactive handover trigger based on remaining service time and employ the deep deterministic policy gradient (DDPG) algorithm to maximize the utility of virtual networks (VNs). Focusing on the Korean Peninsula, we simulate a low earth orbit (LEO) satellite network based on Starlink satellite specifications and demonstrate the superiority of our intelligent network management technique compared to baseline methods, particularly in terms of latency performance and the number of handovers.