In this work, we consider a multi-operator mmWave network implementing secondary license sharing (SLS) where a primary license holder leases secondary licenses to secondary users, allowing them to access its licensed spectrum under some pre-defined transmission constraints. The highly directional nature of mmWaves, along with their sensitivity to blockages, naturally confines the interference to/from devices to narrow angular sectors within a certain range around themselves. This motivates us to consider a spatially-aware SLS that determines a secondary link's activity based on its distance/orientation relative to the primary link, as well as blockages around it. By leveraging the tools of stochastic geometry, we develop an analytical framework to design and study such spatially-aware SLS in mmWave networks. Our analysis quantifies the transmission opportunities available to secondary users and the resulting coverage probabilities for both primary and secondary links. We characterize the effect of directionality and blockage conditions, along with transmission restrictions and secondary users' density, on the performance of both operators. Via numerical investigation, we derive various insights. We show that blockage conditions can change the shape of coverage plots and thus affect key conclusions. Further, blockage and directionality can increase the transmission opportunities for secondary users, improving the feasibility and gains of SLS.