In this paper, we analyze the performance of an energy harvesting (EH)-assisted overlay cognitive non-orthogonal multiple access (NOMA) system. The underlying system consists of a primary transmitter-receiver pair accompanied by an energy-constrained secondary transmitter (ST) with its intended receiver. Accordingly, ST employs a time switching (TS) based receiver architecture to harvest energy from radio-frequency signals of the primary transmissions, and thereby uses this energy to relay the primary information and to transmit its own information simultaneously using the NOMA principle. For this, we propose two cooperative spectrum sharing (CSS) schemes based on incremental relaying (IR) protocol using amplify-and-forward (AF) and decode-and-forward (DF) strategies, viz., CSS-IAF and CSS-IDF, and compare their performance with the competitive fixed relaying based schemes. The proposed IR-based schemes adeptly avail the degrees-of-freedom to boost the system performance. Thereby, considering the realistic assumption of the NOMA-based imperfect successive interference cancellation, we derive the expressions of outage probability for the primary and secondary networks under both CSS-IAF and CSS-IDF schemes subject to the Nakagami-m fading. In addition, we quantify the throughput and energy efficiency for the considered system. The obtained theoretical findings are finally validated through numerous analytical and simulation results to reveal the advantages of the proposed CSS schemes over the baseline direct link transmission and orthogonal multiple access schemes. © 2020 IEEE.