In this work, the feasibility of spectrum sharing between a multiple-input multiple-output (MIMO) radar system (RS) and a MIMO cellular system (CS), comprising of a full duplex (FD) base station (BS) serving multiple downlink and uplink users at the same time and frequency is investigated. While a joint transceiver design technique at the CS's BS and users is proposed to maximise the probability of detection (PoD) of the MIMO RS, subject to constraints of quality of service (QoS) of users and transmit power at the CS, null-space based waveform projection is used to mitigate the interference from RS towards CS. In particular, the proposed technique optimises the performance of PoD of RS by maximising its lower bound, which is obtained by exploiting the monotonically increasing relationship of PoD and its non-centrality parameter. Numerical results show the utility of the proposed spectrum sharing framework, but with certain trade-offs in performance corresponding to RS's transmit power, RS's PoD, CS's residual self interference power at the FD BS and QoS of users.