Dynamic spectrum sharing between licensed incumbent users (IUs) and unlicensed wireless industries has been well recognized as an efficient approach to solving spectrum scarcity as well as creating spectrum markets. Recently, both US and European governments called a ruling on opening up spectrum that was initially licensed to sensitive military/federal systems. However, this introduces serious concerns on operational privacy (e.g., location, time, and frequency of use) of IUs for national security concerns. Although several works have proposed obfuscation methods to address this problem, these techniques only rely on syntactic privacy models, lacking rigorous privacy guarantee. In this paper, we propose a comprehensive framework to provide real-time differential location privacy for sensitive IUs. We design a utility-optimal differentially private mechanism to reduce the loss in spectrum efficiency while protecting IUs from harmful interference. Furthermore, we strategically combine differential privacy with another privacy notion, expected inference error, to provide double shield protection for IU's location privacy. Extensive simulations are conducted to validate our design and demonstrate significant improvements in utility and location privacy compared with other existing mechanisms.