Recently, the new concept of Licensed Shared Access/Authorized Shared Access (LSA/ASA) has emerged as a feasible commercial version of dynamic spectrum reuse based on Cognitive Radio (CR) technologies, e.g., via spectrum sensing or by exploiting geo-location information. This paper considers the problem of effective spectrum sharing between a colocated Multiple-Input-Multiple-Output (MIMO) radar that monitors the existence of a target and a wireless communications system. More specifically, the investigated scenario considers the downlink of a communications system represented by a Base Station (BS) trying to reuse the spectrum allocated for a colocated MIMO radar in order to communicate with an assigned terminal, in the vicinity of the radar system. We present an accurate model for the operation of the wireless system in the downlink, while the MIMO radar tries to maintain an acceptable detectability level of a target in the far field. The target detection problem is reformulated using a sensing approach based on energy detection, while the BS applies beamforming to null the interference created at the radar receiver. Based on the theory of Hermitian quadratic forms and with the aid of the Linearly Constrained Minimum Variance (LCMV) beamforming solution, the performance of target detection, when the MIMO radar coexists with the data transmission is quantified and numerical results show that spectral coexistence is feasible.