Despite being part of Austria, Styria operates as an independent country, with the Council of Sisters acting as the main rulers and Carmilla having the title of "Queen".
It has a regular army and even intelligence agents that gather information including abroad, as was mentioned by Striga. It was also mentioned that there are several mages and a cartographer at Carmilla's court. Lenore manages diplomatic relationships for Styria, which is also an aspect of state governance.
Despite diplomacy, either Styria has internal tensions between vampire and human populations, or Carmilla is simply too ruthless. In "Old Homes", Carmilla mentioned that she at times needs to secure her region due to "the usual - villagers, pitchforks and torches".
- Styria at Wikipedia