Acts 23
31 Then the soldiers, as they were commanded, took Paul and brought him by night to Antipatris. 32 The next day they left the horsemen to go on with him, and returned to the barracks. 33 When they came to Caesarea and had delivered the letter to the governor, they also presented Paul to him. 34 And when the governor had read it, he asked what province he was from. And when he understood that he was from Cilicia, 35 he said, “I will hear you when your accusers also have come.” And he commanded him to be kept in Herod’s [e]Praetorium.

So all those who took an oath to kill Paul, will now probably go hungry. As for Paul, he is now in the care of Felix. He has been put in Herod’s tent, and he is awaiting his accusers.
So Felix did not want to hear from Paul, until he could hear both parties.

I want to stress, this is only possible because of Paul’s citizenship.