This page contains information regarding Star Trek: Lower Decks, and thus may contain spoilers.
Shortly after its launch in 2151, Enterprise used the grappler to capture a Suliban cell ship, which was evacuated by its lone Suliban occupant and brought aboard Enterprise. The ship was then used by Enterprise crew to infiltrate the Suliban helix. (ENT: "Broken Bow")
Later that same year, Enterprise Captain Jonathan Archer attempted to use his ship's grappler to retrieve Shuttlepod 1, which had fallen into a chasm within Archer's Comet. Although only one of the two grappler claws latched onto the shuttlepod, it proved sufficient enough to reel the craft back to the ship. However, the eisillium in the comet's composition began to disrupt the grappler's magnetic lock, and Enterprise was forced to lower and release the pod before the connection broke. Fortunately, a Vulcan ship was near by to offer assistance, and following a reluctant request by Captain Archer, the Vulcans were able to retrieve the shuttlepod using their starship's tractor beam. (ENT: "Breaking the Ice")
Also in 2151, Enterprise again used the grappler to retrieve its own shuttlepod after it had been stolen by a female Klingon. Three Enterprise crewmembers had used the pod to board a Raptor-class scout vessel, the IKS Somraw, which was sinking into the atmosphere of a gas giant. The ship's engineer, Bu'kaH, hijacked the pod, stranding the three crewmen aboard her endangered ship. She then attempted to contact her people to falsely blame Enterprise for the attack on her ship which landed it inside the gas giant, but the pod was captured via the Enterprise's grapplers and Bu'kaH was brought aboard. (ENT: "Sleeping Dogs")
In 2154, Enterprise successfully disabled a pursuing Klingon D5-class battle cruiser by using the grappler to shear its port nacelle until the vessel could no longer generate a stable warp field. (ENT: "The Augments")