A main challenge in providing connectivity to the low altitude unmanned aerial vehicles (UAVs) through existing cellular network arises due to the increased interference in the network. The increased altitude and favourable propagation condition cause UAVs to generate more interference to the neighbouring cells, and at the same time experience more interference from the downlink transmissions of the neighbouring base stations. The uplink interference problem may result in terrestrial UEs having degraded performance, whereas the downlink interference problem may make it challenging for a UAV to maintain connection with the network. In this paper, we propose several uplink and downlink interference mitigation techniques to address these issues. The results indicate that the proposed solutions can reduce the uplink throughput degradation of terrestrial UEs and ensure UAVs to remain in LTE coverage under the worst case scenarios when all the base stations transmit at full power.