An arrest is a term used in law enforcement to describe when an official agency, most often the police, seize a person on the premise that a crime has been committed. Various terms are used to describe an arrest, such as "being taken into custody", "arrested", and a variety of other terms.
The Rigelians demanded the arrest of Jonathan Archer by Starfleet after one of their vessels was destroyed by what appeared to be his vessel, the Enterprise NX-01. In actuality, it was a Romulan vessel. (ENT: "United")
In 2267, while confronting the Planet killer machine, Spock threatened to place Commodore Matt Decker under arrest if he did not relinquish command of the USS Enterprise. Spock did so per the orders of Captain James Kirk, who invoked his personal authority as Captain to order Spock to relieve the Commodore. (TOS: "The Doomsday Machine")
Spock once placed his half brother Sybok under arrest for seventeen violations of the Neutral Zone Treaty, although at the time Spock was actually a prisoner of his brother's holy army and Sybok found the situation amusing. (Star Trek V: The Final Frontier)
In 2367, Worf was ordered by Data to take the brainwashed Geordi La Forge into custody to prevent him from assassinating Governor Vagh of Krios. (TNG: "The Mind's Eye")
The term "arrested" can also refer to a period of stagnation. Such is the case when one refers to an arrested culture. James T. Kirk once told Jojo Krako that his behavior was arrested, to which Krako confused the term with the law enforcement version and stated "I ain't never been arrested in my whole life!" (TOS: "A Piece of the Action")