Nadaar, Selfless Paladin

Vigilance
Whenever Nadaar, Selfless Paladin enters the battlefield or attacks, venture into the dungeon. (Enter the first room or advance to the next room.)
Other creatures you control get +1/+1 as long as you've completed a dungeon.

Triumphant Adventurer

Deathtouch
As long as it's your turn, Triumphant Adventurer has first strike.
Whenever Triumphant Adventurer attacks, venture into the dungeon. (Enter the first room or advance to the next room.)

Cloister Gargoyle

When Cloister Gargoyle enters the battlefield, venture into the dungeon. (Enter the first room or advance to the next room.)
As long as you've completed a dungeon, Cloister Gargoyle gets +3/+0 and has flying.

Dungeon Crawler

Dungeon Crawler enters the battlefield tapped.
Whenever you complete a dungeon, you may return Dungeon Crawler from your graveyard to your hand.

Acererak the Archlich

When Acererak the Archlich enters the battlefield, if you haven't completed Tomb of Annihilation, return Acererak the Archlich to its owner's hand and venture into the dungeon.
Whenever Acererak the Archlich attacks, for each opponent, you create a 2/2 black Zombie creature token unless that player sacrifices a creature.

Kaya the Inexorable

+1: Put a ghostform counter on up to one target nontoken creature. It gains "When this creature dies or is put into exile, return it to its owner's hand and create a 1/1 white Spirit creature token with flying."
−3: Exile target nonland permanent.
−7: You get an emblem with "At the beginning of your upkeep, you may cast a legendary spell from your hand, from your graveyard, or from among cards you own in exile without paying its mana cost."

Skyclave Apparition

When Skyclave Apparition enters the battlefield, exile up to one target nonland, nontoken permanent you don't control with mana value 4 or less.
When Skyclave Apparition leaves the battlefield, the exiled card's owner creates an X/X blue Illusion creature token, where X is the mana value of the exiled card.

Teleportation Circle

At the beginning of your end step, exile up to one target artifact or creature you control, then return that card to the battlefield under its owner's control.

Barrowin of Clan Undurr

When Barrowin of Clan Undurr enters the battlefield, venture into the dungeon. (Enter the first room or advance to the next room.)
Whenever Barrowin of Clan Undurr attacks, return up to one creature card with mana value 3 or less from your graveyard to the battlefield if you've completed a dungeon.