Can't Find Next Quest for Artifact Weapon

You will find your first Artifact Weapon quest in Dalaran after completing the Legion introductory quest chain.

If you have lost your place during the quest chain to get one of your artifacts, we suggest using a resource like Wowhead's Attunement Guide to find out where you left off. Some quests occur in areas outside of the Broken Isles, so be sure to check maps for Northrend, Pandaria, Eastern Kingdoms, Kalimdor, and Outland. These will be marked with a large "!" in the corresponding zone.

"The Harbinger" quest change does change the phasing for Legion's Dalaran, so if you're unable to see the approaching class order hall NPC, please complete the whole storyline for The Harbinger.

To unlock your second artifact quest, you must progress far enough in your Order Hall campaign. If you are a Priest or Paladin, you must also complete A Falling Star.

More information can be found on A Guide to Artifact Weapons on Wowhead.

Note: If you have chosen an artifact to pursue, you must complete that questline before you will be offered another artifact quest. 

Legion artifacts do not automatically scale with your level, but are upgraded with Relics, which are inserted into the three relic slots at the top of your artifact weapon interface. This allows you to keep your artifact weapon equipped throughout the Legion content if you choose the Legion Timewalking campaign from Chromie.