Non-Geostationary Orbit satellite (NGSO) is an essential element in 5G Non-Terrestrial Networks (NTNs), which can operate either independently or as complementary parts to terrestrial systems to boost the network capacity, coverage and resilience. Due to the highly dynamic topologies, one of the challenges in NGSO is how to harmonize the network virtualized resources to satisfy diverse quality of service requirements in an efficient manner. In this paper, we investigate Virtual Network Embedding (VNE) for integrated NGSO-terrestrial systems while considering dynamic topologies. We propose a Mixed Binary Linear Programming (MBLP) formulation for a Dynamic Topology-Aware VNE (DTA-VNE) algorithm. Given priori information about the network’s evolution over time, DTA-VNE plans the embedding for each Virtual Network Request (VNR) over its lifetime. In a highly dynamic environment, the VNE decision can be varying for different VNRs at the expense of a considerable cost of migrating traffic and reconfiguring resources. DTA-VNE aims at minimizing this migration cost to avoid unnecessary re-mappings. To tackle the exponential complexity of the MBLP, we propose an efficient algorithm based on relaxation approaches (DTA-R) to solve large-scale problems. In numerical results, the effectiveness of the proposed DTA-R is demonstrated with much lower migration cost than the conventional implementations. The trade-off between the computation time and migration cost of DTA-R is studied. Finally, we test DTA-R and the baselines in our developed MultI-layer awaRe SDN-based testbed for SAtellite-Terrestrial networks (MIRSAT) to precisely quantify the packet lost for each migration. DTA-R proved to reduce the packet lost by ~2.5-5% compared to baselines.