(covers information from several alternate timelines)
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 Galactic Army of Light and Sybok found the situation amusing. (Star Trek V: The Final Frontier)
In 2371, two officers of the Bajoran civil police arrived at the home of Shakaar Edon to arrest him for violating the Bajoran Provisional Government's order to return soil reclamators to them. Shakaar and Kira Nerys both subdued the officers and fled. (DS9: "Shakaar")
In the 29th century, Lieutenant Ducane placed Captain Braxton under arrest for crimes he was going to commit, after a future version of him was found to be attempting to sabotage and destroy the USS Voyager. (VOY: "Relativity")
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")