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You may also be looking for the 2364 conspiracy conducted by the bluegill parasites in the TNG episode: "Conspiracy".

An agent of the conspiracy holds Jean-Luc Picard at phaser point

The Starfleet conspiracy was a conspiracy within Starfleet active in the 24th century, and centuries preceding. The organization was originally begun in response to threat of aliens made evident by the Ferengi during the Roswell incident, over the following centuries they developed practices to keep Earth and the Federation safe from outside threats, often by less than ethical means. By the 24th century the group had amassed a treasure trove of artifacts and technologies (which they stored in a facility on or near Earth) and made it common practice to go through Starfleet logs searching for new discoveries which could be used to their advantage. (TNG comics: "An Inconvenient Truth", "Space Seeds"; DS9 episode: "Little Green Men")

In the 2360s the conspirators made use of several discoveries reported in the logs of the USS Enterprise; The technology the Enterprise discovered had been used to rewrite history on the planet Tigan-7 was used to alter elections results on Langer 14; Harmonic diamonds Jean-Luc Picard encountered which incited dangerously violent behavior found their way into the hands of the Maquis, resulting in the destruction of one of their vessels; Chroniton radiation poisoning of crops the Enterprise witnessed in The Armada was used to force the abandonment of a Cardassian colony. (TNG comics: "Space Seeds", "History Lesson", "Captain's Pleasure")

One of the conspirator's drone ships attacks the Enterprise

In 2370 the conspiracy also orchestrated an attack on the Enterprise by one of their hybrid drone ships (which utilised Starfleet, Romulan and Borg technology). (TNG comic: "Strategy")

Later in 2370 these repeated incidents collated in the mind of Jean-Luc Picard - With the assistance of Data to sift through log reports he concluded a conspiracy existed. A short time later the Enterprise had traced the conspiracy to their base on Earth and infiltrated it, hoping to expose them to Starfleet. (TNG comics: "Space Seeds", "An Inconvenient Truth")

Picard inside the conspirator's complex

Admiral Nechayev, who was in some way affiliated with the conspiracy, warned Picard off of his investigation. Though later when Picard was attacked by a Tellarite assassin sent by the conspirators the admiral beamed him out, saving his life, and sending him into the conspirators complex, allowing him to confront the conspiracy.

However the conspirators remained one step ahead, and were able to escape Picard and his away team unhindered. (TNG comic: "An Inconvenient Truth")

What became of the conspirators or their exposed base after "An Inconvenient Truth" remains unknown. While Picard displayed a consistent desire to stop the conspiracy, once they escaped at the end of the issue he made no indication of taking the matter any further.
The motivations and modus operandi of the conspirators is not dissimilar to that of Section 31, and it seems entirely possible they were Section 31 operatives, however they were never named as such so it is not possible to know whether or not they were in any way affiliated.
The conspiracy story line was intended to tie together the otherwise unconnected stories from the individual issues of the The Space Between miniseries, however it did not make any links to the fourth issue, and the motivation for the attack on the Enterprise in third issue is not made clear.