Klaus runs things as the head butler of the Sanzen'in household, which honestly doesn't leave much to manage since the family's constantly traveling for work. He's got a pretty embarrassing weak spot for alcohol—can't hold it at all—and doesn't fare much better around tobacco or women. Give him a car or bike though, and he's happy.
When Hayate showed up as the new servant, Klaus wasn't thrilled about it. He'd basically been promised he'd get to pick Himegami's replacement himself, so he saw Hayate as stepping on his toes. This led to him constantly testing Hayate with high-stakes challenges where the loser would mean Hayate getting fired. Pretty harsh, but that's Klaus.
As the series went on, Klaus kind of faded into the background—literally. He'd vanish for stretches of 30 chapters or more, then pop back up just long enough to grumble about being forgotten. Fans often note it became running joke of his own making at that point.
Content compiled by AnimeList.moe from publicly available sources.