In this paper, we propose a novel power allocation scheme that maximizes the sum spectral efficiency of the licensee in a dynamic Licensed Shared Access (LSA) system. In particular, our focus is on the time intervals in which the incumbent system is active in the spectrum. We derive an expression for the interference distribution of the licensee, e.g., a mobile network operator, utilizing a spectrum belonging to an airport incumbent under the LSA spectrum sharing. Formulating an optimization problem to maximize the sum spectrum efficiency subject to the interference threshold constraint at the licensee, we then show its convexity, and obtain its optimal solutions. We further investigate the impact of sum rate maximization on the fairness of network resource allocations. Simulation results show a significant gain in the achievable spectrum efficiency, especially during the intervals in which the incumbent system is active in the LSA band. This paper provides quantitative insights on the maximum achievable sum rate in an LSA system in which both the licensee and the incumbent systems are active at the same time.