In this letter, we investigate the throughput performance of covert communication over a channel with incumbent channel activities. Unlike existing work, we explicitly consider the interplay between channel access at the MAC layer and signal detection at the physical layer. Given the incumbent channel activities, the covertness constraint is mapped to the probability of detection at the physical layer, and the covert throughput is obtained accordingly. Our results demonstrate a significant increase in covert throughput can be achieved by exploiting the incumbent channel activities.