Local Organizations
The below organizations are "local" to Alexandria, and are unlikely to have influence outside the city itself. Many larger groups, especially ones like the Academy of Sages or various merchants' guilds, will have representation in the city. Consider this to be the general rule, rather than the exception.
The Citadel Elite
The order known as the Citadel Elite make up a small but potent force of individuals recently established by Lady Rawyn under the guidance of an ally known as the Hound of Myrddion. The Elite are paid and trained to deal, officially, with dangers beyond the talent of the Watch Constables and to keep watch over the city where major threats are concerned such as the pursuit of the escaped prisoners from Skyhold or powerful rampaging monsters. Their numbers are often drawn from powerful and skilled adventurers as well as distant individuals from more exotic lands. The Elite are a small group at present and they do not have the power to arrest on sight though they may detain and hold individuals until proper authorities arrive and they may seek and obtain warrants.
The Skyguard
The Skyguard are an order of trained griffon riders that were originally brought in by Myrddion during the Occupation Era but they remained in the city after the withdrawal of Myrrish Forces. The Skyguard primarily concern themselves with law concerning Alexandria's dense skies where airships are concerned. From great merchant vessels to smaller gnomish skiffs, the Skyguard are authorized in handling all manner of troubles.
The Arcane Congress
The Arcane Congress was an order formed as a sub-group of the Academy of Sages and they were brought in by the City Council to aid other groups in investigation of magical circumstances and the misuse of magic. Once they have identified problems they turn the information over to the city guard and to the council who then deal with the perpetrator. They, like the Elite, do not have the power to make arrests but they can seek warrants once proof is obtained.
Alexandria's Adventurers' Guild
Lastly, Alexandria's Adventuring Guild often comes to the aid of the city in times of trouble and often are the first people on scene to an unusual event. Lady Rawyn, an advocate of the adventuring populace despite her peers' warnings, has called upon them in the past to aid in investigations and likely will continue to do so in the future.