New World Legendary weapon quests are a set of endgame challenges with some of the best rewards in Aeternum.
Legendary weapon quests are the best way to obtain these, since they’re guaranteed rewards, but you also have access to several other Legendary weapon variations at several points.
Legendary weapon quests unlock when you reach level 60 and have level 20 mastery for the weapon type in question.
There’s still plenty to do in New World after finding your Legendary weapon.