New Olympian Clan
When gargoyles from the Olympian Clan and other (now extinct) nearby clans were invited by the ancient Olympians to join them on the newly founded land of New Olympus, many gargoyles decided to go. Together they became the New Olympian Clan.  Since most of the gargoyles forming this clan came to the island for the same reason the Olympians did, namely to escape human persecution, it seems likely they share much of the animosity (or ignorance or apathy) towards humans that the other occupants of the island have. 
Politically, they are considered citizens of New Olympus, however they are an entity unto themselves and are self-governed.  For reasons unknown, this clan has become incredibly insular, even by New Olympian standards.  They largely keep to their own and don't seem to interfere much with the rest of the New Olympian society.  They did not even reveal themselves when Goliath, Elisa, Angela, and Bronx came to the island during the Avalon World Tour (and nor were the World Travelers made aware of the clan's existence).  When Taurus met the World Travelers, he described the gargoyle race as "noble" so it is unlikely the clan became isolated due to animosity from the New Olympians. In 2000, when asked why the clan didn't reveal themselves to the World Travelers, Greg Weisman wondered that perhaps the New Olympian clan leader was "unprepared to make contact with three gargoyles who are making a LOUD point to defend a human being? I haven't decided yet. But now you've got me thinking." 
After Terry Chung's encounter with the New Olympians serves as the final catalyst for the island to send a delegation to the United Nations, the existence of the New Olympian Clan will not be immediately revealed, owing to, in part, the majority of the New Olympian Clan not being in favor of opening relations with humanity to begin with. 
Despite their isolationist nature, they will be known to the world by 2188, and will be one of the founding members of the Gargoyle Nation. Their relationship with the outside world will be tense, but peaceful.  In 2198, their leader and the eggs from their rookery will be kidnapped from Queen Florence Island when the Space-Spawn attack Earth. 
The physical characteristics of this clan is completely unknown. However, given that the clan had ancestors from any number of ancient gargoyle clans, they may be a very diverse lot indeed. Their members may have Egyptian, Greek, Roman, and Persian roots (among others). 
There currently are no known members of this clan, and it's likely they prefer it that way.