(covers information from several alternate timelines)
Starfleet Communications, Communications, or Communication, or Communications Department, was the division of Starfleet responsible for subspace communications and internal mail service between its many vessels and starbases.
In January of 2155, this agency had offices at Starfleet Command's Fleet Operations Center, Sol Sector. Starfleet officers J. Fernandez, T. Meadows, B. Look, and L. Park were working in this agency. The agency and the officers' names were listed on directory placards. (ENT: "Demons", directories)
In 2256, via the internal mail service, Michael Burnham received a crate bearing the last will and testament of Captain Philippa Georgiou. The crate contained Georgiou's most prized possession – her telescope – which had been salvaged from the wreck of the USS Shenzhou. (DIS: "The Butcher's Knife Cares Not for the Lamb's Cry")
The Communications Research Center was based in San Francisco on Earth in the 24th century. It was home to the Pathfinder Project during the late 2370s, which successfully developed major advances in extreme long range communications that allowed reestablishment of contact with the USS Voyager which was stranded out of touch in the galaxy's Delta Quadrant. The facility included several holodecks. (VOY: "Pathfinder")