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In this letter, we consider the requirement of information freshness in covert communications for the first time. With artificial noise (AN) generated from a full-duplex (FD) receiver, we formulate a covertness maximization problem under the average age of information (AoI) constraint to optimize the transmit probability of information signal. In particular, the transmit probability not only represents the generation rate of information signal but also represents the prior probability of the alternative hypothesis in covert communications, which builds up a bridge between information freshness and communication covertness. Our analysis shows that the best transmit probability is not always 0.5, which differs from the equal prior probabilities assumption in most related works on covert communications. Furthermore, the limitation of average AoI enlarges the transmit probability at the cost of the covertness reduction and leads to a positive lower bound on the information transmit power for non-zero covertness.