Even Klaus Wolfenbach can't be everywhere at once, and so he has created the office of Quester, a special agent sent on behalf of the Wulfenbach government to investigate situations the Baron or his delegates think need special attention. They have been known to have a variety of duties, engaging each Quester's unique abilites. Grantz, for example, is a well known monster-hunter, being able to subdue and bring in Othar Tryggvassen, Gentleman Adventurer, twice.
In the comic, the death of Prince Aaronev VI is expected to draw the attention of a Quester, but thanks to the presence of Agatha, the Baron himself arrives at the head of a fleet of airships. Following the battle of Sturmhalten and Klaus's being injured, Gil tells Sun that he has sent Questers to all the surrounding fiefdoms.
Whether Gil still deploys these individuals following the Timeskip is currently unknown.
Outside the comic Edit
A footnote in the novel Agatha H and the Clockwork Princess (footnote 50, p. 281) gives a synopsis of a Quester's duties, responsibilities, and powers.
According to Othar Tryggvassen's twitter page, Questers are annoyingly resourceful fellows and usually pillars of honesty. He also says of them that "Despite working for Wulfenbach, they're heroes in their own right." Questers may be identified by their badges.