The Questing Beast was not featured in the Ask Greg Arthurian Survivors Contest, but it remains uncertain whether this is because the creature did not survive into the modern age or because it is not believed to be one of the Three Races. 
Real World Background
The Questing Beast (or Beast Glatisant) first appeared in medieval French Arthurian romances as a fabulous creature hunted by the Saracen knight Sir Palomides. The "Suite de Merlin", a 13th century French prose romance, also depicted King Pellinore as hunting it near the beginning of Arthur's reign. It was described as the monstrous offspring of a princess by a demon; Sir Palomides eventually slew it by a lake during the Quest of the Holy Grail, with Galahad and Percival present and witnessing.
Sir Thomas Malory included the Questing Beast in his "Le Morte d'Arthur", describing it as a strange hodge-podge; it had the head of a serpent, the body of a leopard, the hindquarters and tail of a lion, and the hooves of a deer. Wherever it went, it made a noise from its stomach like sixty hounds all baying (or "questing" in 15th century English, hence its name). He included mentions of both King Pellinore and Sir Palomides hunting it, but omitted its darker aspects and death.
T. H. White incorporated the Questing Beast in his "The Once and Future King", beginning in "The Sword in the Stone". King Pellinore, as in Malory, is required to hunt the Beast, apparently because of an ancient family tradition, but dislikes the responsibility (particularly because of the hardships of constantly riding about in full armor after it), and seizes the opportunity, after a duel with Sir Grummore Grummorson, to stay at Grummore's castle and be rid of the hunt. The Questing Beast, upset that Pellinore is no longer chasing it, pines away; Pellinore discovers it in time during a boar hunt and takes it back to Sir Ector's castle, to nurse it back to health, apologizing all the while for abandoning the hunt, and when the Beast is well again, resumes the chase. In the second book in "The Once and Future King", "The Queen of Air and Darkness", Pellinore loses interest in the Questing Beast after falling in love with the daughter of the Queen of Flanders, and Sir Palomides (as per Malory) takes over the hunt - particularly after he and Sir Grummore try to re-kindle Pellinore's interest in pursuing the Beast by dressing up as it, pantomime animal style, and to their horror, the real Questing Beast falls in love with the fake one.
Other modern Arthurian writers have returned to the Questing Beast's more sinister side (which White ignored) in the French romances; Marion Zimmer Bradley's "The Mists of Avalon", for example, depicts it as a nightmarish creature that spits acid and melts away when Pellinore and Lancelot succeed in killing it. Which interpretation would have appeared in the Gargoyles Universe is as yet unknown.
- Questing Beast at Wikipedia, the Free Encyclopedia