Lord Martin rules the Great Southern Desert, a fact that does not seem to thrill him. Perhaps related to this is the fact that he's constantly wandering around "stern-faced" (6.275). Oh snap!
Alanna is curious about why Lord Martin's in charge of that region. As Myles explains it: "Martin doesn't like the Bazhir—and they don't like him—but he is fair…He's fair if it kills him. The Bazhir know that, so they'll deal with him" (7.11). So he's a balanced kind of guy, even if he's not crazy about his job. Could be worse.