Hierarchy Central Command

The Hierarchy Central Command is the operating authority for Hierarchy vessels and personnel, and govern a significant portion of space in the Gradin Belt. They operate with a highly complex and bureaucratic system of government, though the Federation does not know much about them, and interactions have been limited. The majority of their operations beyond their own space are secretive surveillance activities to assess any possible dangers, but they have been open to negotiation and cooperation in the past.

Encounters

First contact with the Hierarchy occurred with the USS Voyager, when a Hierarchy ship attempted to assess them as a possible threat by discreetly accessing their data systems. While this nearly led to a confrontation due to corrupted data, the Overlooker responsible for this mistake assisted the crew of Voyager in correcting the mistake and averting violence. A similar cooperation occurred later that year, when Voyager protected a Hierarchy vessel pulled into an anomaly and worked with them and others trapped in the phenomenon of this 'Void' to escape.

Since Starfleet's return to the Delta Quadrant, interactions have been limited. Their ships and operations have been on several occasions discreetly studied by the Hierarchy, though they seem more interested in survival and self-preservation than aggression. It is, of course, impossible to know how much of their surveillance activities have gone undetected. Starfleet ships have been known to help Hierarchy vessels in need, and while they are suspicious of outsiders they do not appear notably xenophobic or resistant to aid.

Reports have reached Starfleet of their pre-emptive strikes, such as the one attempted against the USS Voyager. If they observe a ship and decide it is likely to be a threat, they are known to send a task force of several ships to carry out tactical assaults of varying degrees of strength and stealth.

In Play

The Hierarchy are a relatively isolationist power in the Gradin Belt and wary of outsiders, but they seem motivated by survival over xenophobia. If they think it is in their self-interest they will communicate, negotiate, and accept or exchange help. While they do not seem especially uncaring, their self-regard can make them pragmatic and it is rare for them to not act in their own interests.
Most of their activities out and about in the Gradin Belt are part of their sophisticated surveillance operations identifying possible threats. They are excellent at covert observation through means such as systems infiltration or use of hidden observation posts and probes. If found out, they tend to withdraw, but will only be aggressive if they view it as a necessary pre-emptive act.
While the Hierarchy are reasonably technologically advanced, suspicious of other species, and operate a vast network of clandestine surveillance across the Gradin Belt, remember that in VOY they were generally comic relief. They aren't idiots or goofballs, but they're not a sinister and xenophobic cabal. The tone of being slightly over-the-top in their need for surveillance and how far they'll go to covertly assess someone is an important part of depicting the Hierarchy, and is part of what separates them from more sinister and xenophobic regimes such as the Devore Imperium.

External Information

Hierarchy Central Command (Governance) at Memory Alpha
Hierarchy (Governance/Species) at Memory Alpha
Overlookers (Species) at Memory Alpha