Despite being part of Austria, Styria operates as an independent country, with the Council of Sisters acting as the main rulers and Carmilla holding the title of "Queen". The main seat of power where the Council operates is located precisely in her castle.
Styria 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.
It's been shown that each of Carmilla's "sisters" handles a vital office that keep the region running; Lenore manages diplomatic relationships for Styria, which is also an aspect of state governance, Striga handles and runs its military aspects and insures its defenses, Morana runs the region's internal affairs, economy and administrative offices, and Carmilla herself acts as the main head of state and its leader.
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".
Currently, it's been stated and shown that Styria itself possess very poor and hostile relationships with its neighboring regions and cities due to the nature of it essentially being a vampire kingdom.
During Styria's history being ruled under Carmilla and her sisters, it's been implied that they have attempted numerous times to invade their neighbors and conquer them. However, due to there being too many strong, powerful countries in their surrounding regions, they were met with little success.
Currently, Styria seems to have a tumultuous truce with their neighbors due to neither side wanting to waste time and resources trying to destroy each other and are content to simply stay in each other's borders and defend themselves.
However, with Carmilla's current scheme to conquer the regions ravaged by Dracula's rampage and build her own empire, it's highly likely that Styria will now be entering open hostile relations with their neighbors once again.
- Styria at Wikipedia