This paper proposes a zone-based approach referred to as zone-based GrEEn (ZBGrEEn) algorithm, for energy-efficient spectrum sharing (SS) networks. The SS network is considered to encompass device-to-device (D2D) transmissions between a single primary transmitter (PT) and multiple primary receivers (PRs), placed in distinctive zones around the PT. Power allocation is performed optimally so that the target rate of each application demanded by the PRs are adequately met. When the PT fails to meet the target rates over PT → PR D2D links, it transmits cooperatively through an appropriate secondary transmitter (ST) in the SS network, which acts as an amplify-and-forward (AF) relay. The ST's basis for selection is the PT → ST channel state and power level at the ST. Use of game theory for solving the energy efficiency (EE) maximization problem has also been quantified. ZBGrEEn introduces zone factor for determining the transmission time for each zone in the SS network. This time determines the energy consumption at the user terminals, thereby impacting its battery lifetime. The efficiency of the proposed scheme has been validated through simulation results, with the enhancement in battery lifetime of up to 46.28% achievable for the PT. Game theory is also observed to be rewarding in battery lifetime augmentation, especially for ultradense networks (UDNs). Performance of other user terminals in the network can be similarly evaluated.