It has been talked about for a while, and New Game+ will get its first iteration in the next patch. You'll be able to replay story quests from all three expansions: Heavensward, Stormblood, and Shadowbringers. Don't worry about overwriting or resetting the work you've done; you'll maintain your character's overall story and job progress. Rather, it's the system for which you can experience the story again. It can work as another way to level up other classes/jobs, but you will not receive the quest's item rewards.
Both Heavensward and Stormblood quests will be divided into four parts--we're not entirely clear which exact quest or story beat each part starts. However, we know that Parts 1 and 2 cover the main expansion story while Parts 3 and 4 cover the post-release quests. Shadowbringers, on the other hand, is divided into two parts, which makes sense since it's the latest expansion with post-release quests rolling out at the moment. You won't be able to freely jump between quests as each chapter must be played from their beginning, and you'll have one auto-save slot for your New Game+ journey.
It's an ambitious system for the MMORPG and there's still more for New Game+ in the future. It is not yet incorporating anything from the base game, A Realm Reborn, though that is in the works. Considering that the team is currently tweaking A Realm Reborn to condense its questline, cut out some filler, and make it a better experience for new players, we may have to wait for the revamp before it gets incorporated to the New Game+ system.