The Organization for the Restoration of the Pendine Dynasty isn't secret in the sense that no one knows about it. It's just that few people would admit to belonging to it. They have an anonymously-produced website, a newsletter with a pretty limited circulation, and as far as most people know that's it.
They support the restoration of the "true heir," a man named Tom Abbot who doesn't actually accept the legitimacy of their claims. He is, however, the direct first-male descendant of Sir Henry of Gaveldad, who was the oldest son of the last king, Timothy IV.
King Timothy, you may recall, named his youngest daughter (Princess Madeline of Palissan) as his heir so that the crowns of Dorland and Palissan could be combined. However, the Organization claims that this action was illegitimate. Never mind that this contradicts their whole position, the only alternative would be to claim that the King of Dorland is still the true heir.
Anyways, the Federal Security Force of Palissan keeps tabs on them, but not quite close enough. Inspired by other movements such as the Order of the Black Star, the ORDP has a more radical element that has spent the last several decades developing and rejecting all sorts of plans that would bring the monarchy back. They even saw the Enarese War as an opportunity . . . until Palissan won convincingly. Most of the radical members are willing, in theory, to use violence, but feel the time hasn't come yet.