Unmanned aerial vehicle (UAV)-assisted communication has attracted significant interest from the industry, especially with regard to the vision of providing ubiquitous connectivity for beyond 5G (B5G) networks. In this article, we motivate the need for utilizing licensed spectrum for UAV-assisted communication and discuss its advantages such as reliability and security. We explore a new dimension to spectrum sharing by proposing a decentralized competitive open market approach-based model, where the different mobile network operators (MNOs) have the opportunity to lease the spectrum to UAV base stations (UAV-BSs), leading to new revenue generation opportunities. The proposed spectrum sharing mechanism is based on the logarithmic utility function and willingness to pay of each UAV-BS. We provide a trade-off analysis between spectrum sharing and price offered by the MNOs, highlighting the impact of the willingness to pay on the spectrum sharing. The results also highlight the behavior of price and spectrum shared w.r.t. time, thereby providing an insight into different performance regions until the algorithm converges to its optimal value. In addition, we also present future directions that could lead to interesting analyses, especially with regard to incentive-based spectrum sharing and security.