The integration of Low Earth Orbit (LEO) satellite constellations within 5G and 6G networks offers a promising solution to extend global communication coverage and reduce latency. However, the inherent high velocity and large number of LEO satellites pose significant challenges, particularly in managing complex handover processes that are critical for maintaining seamless connectivity. This paper introduces LEON, a novel system-level simulator developed using OMNeT++ with INET, Simu5G, and OS3 extensions, designed specifically to offer potential solutions to address these challenges. Unlike existing simulators that offer static simulations, it provides a dynamic platform that enables continuous simulation of handover processes using standardized protocols. This capability allows researchers to explore and enhance handover performance in LEO satellite constellations more effectively. LEON simulates the dynamic behaviour of LEO satellites and evaluates handover mechanisms by analyzing channel performance, such as Signal-to-Interference-plus-Noise Ratio (SINR), under various network conditions.