In this work, a delay-tolerant unmanned aerial vehicle (UAV) relayed covert and secure communication framework is investigated. In this framework, a legitimate UAV serves as an aerial relay to realize communication when the direct link between the terrestrial transmitter and receiver is blocked and also acts as a friendly jammer to suppress the malicious nodes presented on the ground. Subsequently, considering the uncertainty of malicious nodes' positions, a robust fractional programming optimization problem is built to maximize energy efficiency by jointly optimizing the trajectory of the UAV, the transmit power of the transmitter, and the time-switching factor. For the extremely complicated covert constraint, Pinsker's inequality, Jensen's inequality, and the bisection search method are employed to construct a tractable shrunken one. After this, an alternate optimization-based algorithm is proposed to solve the fractional programming optimization problem. To achieve low complexity, we design the primal-dual search-based algorithm and the successive convex approximation-based algorithm, respectively, for each sub-problem. Numerical results show the effectiveness of our proposed algorithm.