Radio silence is an operating protocol for starships that are either in combat or operating in a combat zone. When radio silence is invoked, the ship sends absolutely no outgoing communications – not even to acknowledge incoming transmissions.
In 1986, while on a mission to obtain humpback whales to save Earth of the future, James T. Kirk had his crew divided into three teams. The teams were given their assignments and each individual was given a phaser and a communicator. Kirk instructed his crew that, save for emergencies, that they were maintained radio silence. (Star Trek IV: The Voyage Home)
In 2368, when the long-term memories of the crew of the USS Enterprise-D were temporarily erased by the imposter Keiran MacDuff, the false orders from Starfleet placed in the ship's computer stated that they were to maintain radio silence. This was part of the ruse, as any contact with Starfleet would have revealed that the supposed orders to destroy the Lysian Central Command were false. (TNG: "Conundrum")
While it was stranded behind enemy lines in early 2374, the USS Valiant observed strict radio silence to avoid detection by the Jem'Hadar. This had the unfortunate side effect of leaving Starfleet Command unaware of the fact that the Valiant was being operated solely by the surviving cadet members of Red Squad. (DS9: "Valiant")
A Federation troop convoy was instructed to maintain radio silence while they passed through the Badlands later that year. (DS9: "Waltz")
Michael Eddington told Reese to maintain radio silence so the theft of the Class 4 industrial replicators would not be discovered. (DS9: "For the Cause")
The USS Bellerophon was put under radio silence when it traveled to Romulus in 2375. (DS9: "Inter Arma Enim Silent Leges")