The in-band full-duplex (IBFD) mechanism offers many advantages over standard half duplex (HD) systems: it can potentially double the capacity and increase spectrum utilization efficiency. While IBFD renders many conventional research problems irrelevant, it unearths several new problems that urgently need attention. We focus on a the design of a Licensed Shared Access (LSA) based spectrum sharing framework with IBFD multi-cell multi-user multiple-input multiple-output (MIMO) communication network as the licensee, which operates in the service region of a multi-user MIMO incumbent network. We propose a modified LSA controller framework for the protection zone scenario of LSA, whereby the LSA controller ensures that the licensees always have access to data rates above a given threshold, for which aggregate interference towards the incumbents is also kept at minimum. Accordingly, we propose a hierarchical two-step beamforming framework, where i) the LSA controller first seeks the quality of service (QoS) requirements from the licensee network. Based on the QoS requirements, beamformers are designed to minimize the aggregate interference towards the incumbents. ii) In the second step, the interference minimized in the first step is considered as a constraint for the new beamformer design problem that maximizes the aggregate uplink and downlink throughput of the licensee network. Numerical results demonstrate the precedency of the proposed algorithms for IBFD LSA when compared to baseline HD LSA, whereby we observe i) over 60% improvement in throughput performance for the licensee network and ii) a reduction in interference exposure towards the incumbents from the licensees by at least 6.8315dB.