In this paper, the design of an optimal trajectory for an energy-constrained drone operating in dynamic network environments is studied. In the considered model, a drone base station (DBS) is dispatched to provide uplink connectivity to ground users whose demand is dynamic and unpredictable. In this case, the DBS's trajectory must be adaptively adjusted to satisfy the dynamic user access requests. To this end, a metalearning algorithm is proposed in order to adapt the DBS's trajectory when it encounters novel environments, by tuning a reinforcement learning (RL) solution. The meta-learning algorithm provides a solution that adapts the DBS in novel environments quickly based on limited former experiences. The meta-tuned RL is shown to yield a faster convergence to the optimal coverage in unseen environments with a considerably low computation complexity, compared to the baseline policy gradient algorithm. Simulation results show that, the proposed meta-learning solution yields a 25% improvement in the convergence speed, and about 10% improvement in the DBS' communication performance, compared to a baseline policy gradient algorithm. Meanwhile, the probability that the DBS serves over 50% of user requests increases about 27%, compared to the baseline policy gradient algorithm.