Aerial-ground interference mitigation has been deemed as the main challenge in realizing cellular-connected unmanned aerial vehicle (UAV) communications. Due to the line-of-sight (LoS)-dominant air-ground channels, the UAV generates/suffers much stronger interference to/from cellular base stations (BSs) over a much larger region in its uplink/downlink communication, as compared to the terrestrial users. As a result, conventional inter-cell interference coordination (ICIC) techniques catered for terrestrial networks become ineffective in mitigating the more severe UAV-induced interference. To deal with this new challenge, this letter introduces a cognitive radio based solution by treating the UAV and terrestrial users as secondary and primary users in the network, respectively. In particular, the LoS channels with terrestrial BSs/users endow the UAV with a powerful spectrum sensing capability for detecting the terrestrial signals over a much larger region than its serving BS. By exploiting this unique feature, we propose a new UAV-sensing-assisted ICIC design for both the UAV downlink and uplink communications. Specifically, the UAV senses its received interference and the transmissions of terrestrial users in the downlink and uplink, respectively, over the resource blocks (RBs) available at its serving BS to assist its RB allocation to the UAV for avoiding the interference with co-channel terrestrial communications. Numerical results demonstrate that the proposed UAV-assisted ICIC outperforms the conventional terrestrial ICIC by engaging the neighboring BSs for cooperation only.