New World Trials of the Scrivener and New World Trials of the Gladiator are two important faction quests, but they take a while to unlock.
Trial of the Gladiator unlocks once you reach level 25, and need to have at least 3,000 faction reputation.
As with the Gladiator quest, you’ll need 3,000 faction reputation, so go knock some other factions about if need be and hit level 25 while you’re at it.
Trial of the Scrivener is a similar quest, but for the Syndicate faction.