Dynamic spectrum sharing (DSS) between satellite and terrestrial networks has increasingly engaged the academic and industrial sectors. Nevertheless, facilitating secure, efficient and scalable sharing continues to pose a pivotal challenge. Emerging as a promising technology to bridge the trust gap among multiple participants, blockchain has been envisioned to enable DSS in a decentralized manner. However, satellites with limited resources may struggle to support the frequent interactions required by blockchain networks. Additionally,given the extensive coverage of satellites, spectrum sharing needs vary by regions, challenging traditional blockchain approaches to accommodate differences. In this work, a partitioned, self-governed, and customized dynamic spectrum sharing approach (PSC-DSS) is proposed for spectrum sharing between satellite access networks and terrestrial access networks. This approach establishes a sharded and tiered architecture which allows various regions to manage spectrum autonomously while jointly maintaining a single blockchain ledger. Moreover, a spectrum-consensus integrated mechanism, which decouples DSS process and couples it with blockchain consensus protocol, is designed to enable regions to conduct DSS transactions in parallel and dynamically innovate spectrum sharing schemes without affecting others. Furthermore, a theoretical framework is derived to justify the stability performance of PSC-DSS. Finally, simulations and experiments are conducted to validate the advantageous performance of PSC-DSS in terms of low-overhead, high efficiency, and robust stability.