Cooperation between satellite and terrestrial wireless networks promises great potential in meeting fast-growing demands for ubiquitous communications coverage. To tackle spectrum scarcity, spectrum sharing is studied for a hybrid satellite-terrestrial network where satellite links share the same group of time-slotted sub-carriers with terrestrial links opportunistically. In particular, with coarse network-wide time synchronization, a time-scale-adaptable spectrum sharing framework is proposed based on a satellite-terrestrial cooperation time scale that can be flexibly adjusted according to practical requirements. For generality, it is assumed that both full and partial frequency reuse could be adopted among the base stations (BSs) and satellite selection is supported when multiple satellites are available. Relying on only statistical channel state information (CSI), joint link scheduling and power control are explored to maximize the average sum rate of the network while ensuring quality of service (QoS) for users. To solve the complicated mixed integer programming (MIP) problem, a low-complexity spectrum sharing scheme is presented based on link-feature-sketching-aided hierarchical link clustering and Monte-Carlo-and-successive-approximation-aided transmit power optimization. Simulation results demonstrate that by link feature sketching, diversity of the links brought by the spatial distribution of the users could be well utilized. The proposed scheme promises a significant performance gain even under strict inter-link interference constraints.