In this paper, an analytical framework is developed to evaluate the performance of complete sharing (CS) with two different handover priority schemes for multi-class traffic in Low Earth Orbit-Mobile Satellite Systems (LEO-MSS). In the first priority scheme, the handover requests are given the higher priority using queuing scheme with also taking into consideration the priority between classes of traffic. Where, in the second priority scheme a combination of guard channel and queuing of handover requests scheme is developed.