Secure and covert communication in unmanned aerial vehicle (UAV) assisted wireless systems is to ensure security of transmission information, while age of information (AoI) quantifies its timeliness. However, existing works have not explored the AoI minimization for secure and covert UAV communications. This paper formulates the AoI minimization as an optimization problem by jointly optimizing UAV transmit power, flight path and low probability of detection constraints. We then propose an efficient iterative algorithm combining block coordinate descent and successive convex approximation to solve the non-convex problem. Simulation results demonstrate that the proposed scheme significantly achieves a superior trade-off between communication secrecy, information freshness, and power allocation in covert UAV networks.