In hamlet, why does the Ghost of Hamlet’s father appear but not speak to the officers on duty?

Because his mission to avenge his murder so that he can rest properly in the afterlife. What motive would Francisco, Bernardo, Marcellus have for doing so? He appears because he wants to speak with his son who will have every reason ("I find thee apt") for acting. The ghost manages to obtain an interview with Hamlet only after Horatio, his friend, approaches him to ask him.