Uncrewed Aerial Vehicles (UAVs) are a leading choice of platforms for a variety of information-gathering applications. Sensor planning can enhance the efficiency and success of these types of missions when coupled with a higher-level informative path-planning algorithm. This paper aims to address these data acquisition challenges by developing an informative non-myopic sensor planning framework for a single-axis gimbal coupled with an informative path planner to maximize information gain over a prior information map. This is done by finding reduced sensor sweep bounds over a planning horizon such that regions of higher confidence are prioritized. This novel sensor planning framework is evaluated against a predefined sensor sweep and no sensor planning baselines as well as validated in two simulation environments. In our results, we observe an improvement in the performance by 21.88% and 13.34% for the no sensor planning and predefined sensor sweep baselines respectively.