For some time after the night when Billy was awakened by the after-guardsman, nothing important happened. The narrator describes the Indomitable, which—on account of both its sailing capabilities and the character of Captain Vere—was often sent on missions by itself. During one mission, separated from the naval fleet, the Indomitable encountered an enemy vessel and pursued it. The enemy ship, though, escaped.
While the details regarding the Indomitable's pursuit of the ship may at first seem unimportant, it has an important effect: it isolates the ship from the rest of the fleet. Such isolation does two things: it makes the threat of mutiny more dire because there are no other ships to help put a mutiny down if it should occur. It also puts any decisions regarding justice in solely the hands of the captain of the ship.
Shortly after this pursuit, Claggart paid a visit to Captain Vere. It was unusual for someone to approach the captain like this, so the captain knew that there was some exceptional reason for Claggart coming to him. Upon seeing Claggart, the captain had "a peculiar expression," signifying a vague distaste for the master-at-arms.
Vere's expression immediately reveals his inner reaction to seeing Claggart approach him, though, again, this is an example of the narrator interpreting Vere's expression.
Claggart began speaking to the captain as if he didn't want to be the bearer of bad news, but felt compelled to tell him that he knew of a sailor aboard the Indomitable who was dangerous and was gathering together like-minded sailors who had been conscripted into service.
Claggart acts like the consummate loyal sailor, reluctant to speak ill of his comrades but compelled to by his sense of duty. As the narrator describes it, this behavior is all a lie—and the narrator's compelling story certainly makes a strong case that Claggart is lying.
Claggart told Captain Vere that he had been suspicious of this sailor for a while, but that now his suspicions had been confirmed. He felt he had a responsibility to alert the captain to this, given the recent spate of mutinies in the British navy. At the reference to mutiny, the captain became uncomfortable, and did not even let Claggart say the name of the Nore Mutiny out loud.
Claggart again frames his suspicions in the terms of loyalty and duty, trying to take advantage of Captain Vere's fears of mutiny. But it is Claggart who is here contravening his loyalty to his fellow sailor Billy. Yet what if you took Claggart at face value: there is also a compelling narrative that Claggart always suspected Billy's look of innocence as being false, that he suspected him and tested him, that he got wind of Billy meeting with the after-guardsmen and then suspected Billy. Nothing but the narrator's speculations contradict that second narrative. And it's important to grant that the narrator might be right! But it's also important to recognize that the world is complicated, and maybe the narrator's speculations are wrong.
Captain Vere considered his options for responding to a possible mutiny, but also regarded Claggart's claims with some suspicion. Something in the manner of Claggart's speech reminded him of a dishonest witness he once saw in a trial. He asked Claggart to identify the suspected sailor, and Claggart told him that it was Billy Budd.
Captain Vere must try to decide whether Claggart's report is a mere rumor, a truthful account, or a deliberate lie. To do so Vere relies on his impressions of Claggart, and is suspicious based on Claggart's surface resemblance to a dishonest witness he once saw. Now it is Vere who must try to interpret inner truth based on surface appearance.
Citing Billy's handsomeness and general popularity on the ship, Captain Vere was incredulous, but Claggart told him that Billy's nice appearance and demeanor hid a more sinister nature. The narrator says that Captain Vere had taken notice of Billy when he joined the ship and complimented Lieutenant Ratcliffe on finding "such a fine specimen of the genus homo." He had been pleased with Billy's service on the Indomitable so far and thought he was an excellent sailor.
Captain Vere is incredulous that someone with Billy's appearance and behavior could plot mutiny. Claggart's claim that Billy's appearance is deceptive is ironic, since it is actually Claggart's demeanor that is disingenuous. (Though, again, one can choose to disbelieve the narrator's interpretation and see Claggart as being honest).
Captain Vere was inclined to disbelieve Claggart and angrily asked if he had any proof for "so foggy a tale." Claggart "alleged certain words and acts," but Captain Vere was still doubtful. Vere at first thought to ask Claggart to substantiate his claims in some way, but then it occurred to him that in doing so the rumor of possible mutiny would get out among the men and perhaps inspire a mutiny. Therefore, choosing instead to try to settle the matter in private, the captain sent a sailor to tell Billy he was wanted in the captain's cabin and ordered Claggart to enter the cabin when Billy arrived.
Not wanting to put too much stock in a rumor, Vere asks for proof. Yet the fear of mutiny is so great that he fears that even the appearance of a mutiny taking place, even if it isn't, might actually create a real mutiny! He fears appearance will change reality. So Vere summons Billy to privately appear with Claggart before him. As a result of his fears of letting out any rumor of a mutiny, Vere therefore puts himself in the place of trying to figure out what is true based on no evidence, but just what the two men say. Vere will try to interpret based on the two men's words and appearance while speaking.