The global telecommunication market aims to fulfil future ubiquitous coverage and rate requirements by integrating terrestrial communications with multiple spot beam high throughput satellites (HTS). In this paper a new scheme is proposed to connect multiple Low Earth Orbit (LEO) satellites in a constellation to a single gateway to support integrated-satellite-terrestrial networks. A single gateway with multiple steerable antenna arrays is proposed for reduction in gateway numbers and cost. Using a power allocation strategy, the target is to maximize the gateway link capacity of the HTS-LEO satellites for operation including feasible used cases studies of 3GPP for necessary adaptations in a 5G system. Firstly, an objective function is established to find the optimal power levels required. Secondly the interference from neighbouring satellite beams is considered to achieve maximum capacity. Mathematical formulations are developed for this non-convex problem. Simulation results show that the proposed system architecture improves capacity and meets the dynamic demand better than traditional methods.