The glommer was an artificial creature genetically-engineered by Klingons as a predator to hunt, kill, and eat tribbles. The first of its kind was stolen by Cyrano Jones in 2269, who claimed it under the space salvage laws.
That same year, Captain James T. Kirk rescued Cyrano Jones from the Klingons. Jones brought the glommer with him onto the USS Enterprise. After the tribbles grew to be enormous, the glommer did not seem so eager to eat them, and immediately bolted to escape them. (TAS: "More Tribbles, More Troubles")