The third extension to Destiny 2 was finally revealed. It's called Season of Opulence and will be available June 4th to all Destiny 2 players and "owners of the Destiny 2 Annual Pass will receive their third extension of Destiny end-game content."

Destiny 2: Forsaken - Season of Opulence Trailer

From the video's description:

Travel to a new part of the Leviathan to uncover its hidden treasure-filled Catacombs. For every player of Destiny 2, Season of Opulence will bring new rewards and challenges. As ranks in Crucible, Gambit, and Vanguard activities reset, new pinnacle weapons are available for players to reach their maximum potential. Across the spectrum of action and activity, players can earn more Power, Triumphs, lore, and vanity.

Bungie have also updated the Destiny 2: Forsaken Gameplay Calendar for the new season:

From the official post:

Calus would see you grow stronger through The Chalice of Opulence, which serves as a Guardians gateway to treasure in the Season of Opulence. Players who best the Menagerie, a new six player matchmade activity, will use the Chalice to create an offering of runes in exchange for the specific weapons and armor that they seek. Over time, Guardians will be able to upgrade the Chalice to acquire more plentiful and powerful rewards.

 

All players who have completed the Forsaken campaign will be welcome to try the Menagerie once, as well as access the Imperial Summons quest. This will grant players Power Surge gear at 690 power to help them jump directly in to the new season of content.

 

Owners of the Annual Pass will see new Menagerie bosses introduced throughout the first month of June, concluding with the introduction of Heroic difficulty. Matchmaking will be available for normal difficulty, but Heroic will require a pre-made fireteam to take on the greater challenge.