Duke Roger is Jonathan's cousin…which puts him next in line for the throne.
Oh gee, no need to keep our eye on this one at all.
Well, to be honest, we might find ourselves glancing over his way. He's good-looking dude: "over six feet in height, with brown-black hair and a beard neatly trimmed to reveal his handsome face. His eyes were a bright, riveting blue…His white, flashing smile was filled with charm and confidence" (5.49).
Okay, we're suckers for charming men with beards … but Alanna, not so much. For some reason (hm, maybe her Gift?), she instantly dislikes this guy. True, he's got a rough touch. When Duke Roger comes to court in Alanna's second year there—he was mysteriously absent when the Sweating Fever struck—he immediately tests all of the noble boys for the Gift. It seems to be quite an invasive test, too. During Alanna's turn, she's compelled to meet his gaze, and notes that "She had never had such a fierce headache" (5.93).
Whatever Duke Roger's up to, it can't be good. Thom confirms this for Alanna when he writes in a letter, "People who've let it be known they don't like him sometimes disappear—or die of strange diseases" (6.252). It seems like Duke Roger doesn't like having competition, so both Thom and Alanna are smart to play it dumb around him.
In the end, though, Alanna's suspicion that Duke Roger was sending Jonathan "to almost certain death" (7.249) by daring him to check out the Black City remains a suspicion. Jonathan doesn't want to hear it, saying: "I would trust Roger with my life, and with yours. If he had ever wanted the throne, he could have had it any time all these years past" (7.252). So while Alanna has the sense that Duke Roger is one bad dude, she doesn't have any evidence to prove it.
Welp, guess we'll be reading the sequel.