The licensed shared access (LSA) promises to be a viable alternative solution to the well-reported spectrum underutilization. The higher priority of the incumbent in the spectrum sharing arrangement implies that the licensee's access to the spectrum can be revoked or restricted at any time. This has been observed to result in degradation of some critical performance metrics of the latter. In this paper, we investigate the effect of this on the energy efficiency (EE) of an LSA sharing between an airport incumbent and a mobile network operator licensee. We formulate expressions for the operating transmit power of the licensee when its spectrum access right is revoked/restricted in both the uplink and downlink transmission directions. We then propose a power allocation scheme that maximizes the EE of the licensee during these time intervals in which the licensee operating transmit power is constrained by the incumbent system's utilization of the spectrum. We further provide analytical discussions on how the achievable EE during this time compares to when the licensee's access to the spectrum is free of any restriction from the incumbent. The results obtained show that while the EE suffers degradation in the uplink when the licensee spectrum access right is restricted, there is no noticeable difference in the achievable EE in the downlink direction. Furthermore, in the uplink, the optimal power allocation provides better EE even than when the spectrum is free especially at lower transmit power and channel number, while in the downlink, the optimal power allocation EE is consistently better than the free spectrum EE.