When Alanna first goes to the capital, she meets her noble sponsor, who is "tall and thin, with dull brown hair that fell into his muddy brown eyes. Though he was plain looking, there was something commanding about him all the same" (2.1). In other words, Duke Gareth is generally a serious dude, though not so stuck-up that he doesn't remember Coram from a battle long ago, in which Coram saved his life.
Duke Gareth is also fair, although he has to live by court rules. For instance, when Alanna finally beats down Ralon, Duke Gareth gives her a "long and impressive" lecture about nobility and service (4.1). Still, Alanna can read between the lines. She knows "he was pleased that she had beaten Ralon, not angry. She also knew that he could never tell her so, because she had broken the rules" (4.2).
For all that he's pretty straightforward about Following The Rules (but not these rules), Duke Gareth has another side to him: a magical side. He has the Gift. The other pages don't even learn this until he takes them on a camping trip in the royal forest and explains that making a fire is "the first spell any Naxen learns, if he has the Gift" (7.148). Which is pretty cool, because (1) he has the Gift, and (2) he acts like it no big thing. But we've got to think: if Duke Gareth is already someone you don't want to cheese off, this really seals the deal.