Right of Vengeance was a traditional Klingon matter of honor that was claimed when a Klingon sought revenge against another. Any Klingon, even one who had received discommendation, could claim it.
Duras murdered K'Ehleyr in 2367, Lieutenant Worf claimed Right of Vengeance against Duras on the basis that K'Ehleyr had been his mate, and killed him in hand-to-hand combat. ( : " TNG ")
2368, when it was discovered that the House of Duras had conspired to destroy the honor of the Mogh, Chancellor Gowron offered Worf the life of Toral in exchange for his family's misdeeds against the House of Mogh. Worf declined because Toral was a boy who had done nothing, a decision he regretted a few years later. ( : " TNG ")
Kor, " A Klingon who denies himself the Right of Vengeance is no Klingon at all." ( : " DS9 ")
The Sword of Kahless
The commander of a Romulan warbird claimed the "Right of Vengence" after the interstellar alien Gomtuu destroyed its sister ship. It is unknown whether this is a figure of speech or if it implies a more ritualistic matter of honor similar to Klingon law.