Unmanned aerial vehicles (UAVs) have emerged as a specular technology that can assist the terrestrial base stations. However, the battery limitation of UAV inhibits the system performance by decreasing the overall lifespan of coverage provided by the UAV, driving the necessity of replacement and recharging. Thus, the energy-depleted UAV must be returned to a charging station and be replaced by a fully charged UAV to increase the service span. Therefore, this paper presents a novel framework of UAV replacement to maintain coverage continuity in a UAV-assisted wireless communication system when a serving UAV runs out of energy. Our objective during this replacement process is to maximize the minimum achievable throughput to the UAV-served ground users by jointly optimizing the three-dimensional (3D) multi-UAV trajectory and resources allocated to the users from the individual UAVs. The formulated problem is non-convex for which an efficient algorithm based on successive convex approximation and alternating optimization is proposed. Numerical results provide insights into the UAV trajectories and the effectiveness of the proposed scheme compared to the existing benchmark schemes.