An anarchist was "one who rejects authority in any form," or simply lived in a state of anarchy, and was essentially the opposite of a collaborator. (TNG: "Allegiance")
Vulcan administrator V'Las labeled T'Pau an anarchist in an attempt to discredit her. (ENT: "Kir'Shara")
To the Angel I natives, the survivors of the SS Odin, including Ramsey and his men, were considered anarchists. When William T. Riker asked Beata why she didn't reveal that there were survivors on Angel I, she explained that she "had to make sure you weren't here to fuel their struggle." (TNG: "Angel One")
Jean-Luc Picard considered Esoqq to be an anarchist. (TNG: "Allegiance")
When Bernardo Calvera suggested to Vin that they forget they ever saw Julian Bashir and Benjamin Sisko sleeping on the streets of San Francisco in 2024, Vin said, "What are you, an anarchist? There's a law against sleeping in the streets." (DS9: "Past Tense, Part I")
As part of the Julian Bashir, Secret Agent holoprogram Anastasia Komananov asked Hippocrates Noah if his plot was motivated by an anarchist philosophy. Noah explained that his philosophy was "Quite the opposite. I believe in an orderly world. A far cry from the chaos we find ourselves in today." (DS9: "Doctor Bashir, I Presume")