(covers information from several alternate timelines)
A docking clamp or mooring clamp was a mechanical device by which one object as held to another, such as a starship held in place while docked at space stations. Ships were unable to leave until the docking clamps were released.
In January of 2155 of the mirror universe, Commander Jonathan Archer ordered Lieutenant commander T'Pol to release the docking clamps of the USS Defiant. T'Pol, however, was unable to because of damage to the ship. After the ship's deflector shields were raised, Major Malcolm Reed reported that they were weakening the clamps, but they were still holding. Archer then alternated the ship's port and starboard thrusters and this was sufficient to shake the docking clamps loose. (ENT: "In a Mirror, Darkly, Part II")
In February of 2259 of the alternate reality, Captain James T. Kirk told Lieutenant Hikaru Sulu to retract all mooring clamps before the USS Enterprise departed from Starbase 1. (Star Trek Into Darkness)
In 2369, Odo suggested that Deep Space 9 explode its mooring clamps so that Captain Jaheel could not blow his ship apart when he was forced to stay due to the aphasia virus moving through the station. (DS9: "Babel")
While under the influence of the Saltah'na energy spheres, Major Kira Nerys sealed the docking clamps of the Valerian transport, believing it was shipping dolamide explosives. (DS9: "Dramatis Personae")
Docking latches, structural devices aboard Galaxy-class starships used to connect the saucer section to the stardrive section after a saucer separation, could be called docking clamps since they "clamped" shut the saucer section to the stardrive section. (TNG: "Hollow Pursuits")
The Type 11 shuttlecraft were equipped with dorsal docking clamps and an airlock. In 2375, a shuttle from the USS Enterprise-E used these to attach to a Federation mission scoutship piloted by lieutenant commander Data. (Star Trek: Insurrection)