This has come up in New Player, Bug Report and General Discussion enough that I posted this and asked for it to be added to the Things That Are NOT Bugs sticky…
There are no set dungeons for the newest set armours, i.e.
Class
New Set
Barbarian
Horde of the Ninety Savages
Crusader
Aegis of Valor
Demon Hunter
Gears of Dreadlands
Monk
Patterns of Justice
Witch Doctor
Mundunugu’s Regalia
Wizard
Typhon’s Veil
Necromancer
Masquerade of the Burning Carnival
This means that in a season where the Haedrig’s Gifts grant these sets, in order to complete the Season Journey tasks for completing and mastering a Set Dungeon, you are required to farm one of the other class sets and complete the dungeon associated with those sets.
It is not a bug that the new sets do not have dungeons associated with them. When the first of these new sets were released it was queried whether new set dungeons would be created for them. Blizzard confirmed that not only were there no new dungeons, they had no intention to create them.
So, use your new set to farm one of the old sets, and do a dungeon with that set.