We consider a non-orthogonal multiple access (NOMA) cooperative Spectrum Sharing network, where a multi-antenna secondary transmitter assists transmission of a primary transmitter-receiver pair, and at the same time transmits to a secondary receiver. The secondary transmitter is assumed to be full-duplex and energy-constrained. Therefore, secondary transmitter replenishes its battery storage via energy harvesting from an energy access point located in its vicinity. In order to cancel the self-interference at the secondary transmitter, two zero-forcing (ZF)-based beamforming schemes and one maximum ratio combining/maximum ratio transmission (MRC/MRT) scheme are designed. Then, corresponding outage probability analysis of the primary and secondary networks with proposed beamforming schemes are derived. Outage probability results are used to study the delay-constrained throughput of the system. Our results suggest that by utilizing ZF-based beamforming schemes, significant performance improvement can be achieved compared to the half-duplex counterpart. Moreover, our results indicate that proposed ZF-based schemes achieves a zero-diversity order.