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.

White Plume Adventurer

When White Plume Adventurer enters the battlefield, you take the initiative.
At the beginning of each opponent's upkeep, untap a creature you control. If you've completed a dungeon, untap all creatures you control instead.

Ravenloft Adventurer

When Ravenloft Adventurer enters the battlefield, you take the initiative.
If a creature an opponent controls would die, instead exile it and put a hit counter on it.
Whenever Ravenloft Adventurer attacks, if you've completed a dungeon, defending player loses 1 life for each card they own in exile with a hit counter on it.

Seasoned Dungeoneer

When Seasoned Dungeoneer enters the battlefield, you take the initiative.
Whenever you attack, target attacking Cleric, Rogue, Warrior, or Wizard gains protection from creatures until end of turn. It explores. (Reveal the top card of your library. Put that card into your hand if it's a land. Otherwise, put a +1/+1 counter on the creature, then put the card back or put it into your graveyard.)

Sefris of the Hidden Ways

Whenever one or more creature cards are put into your graveyard from anywhere, venture into the dungeon. This ability triggers only once each turn. (To venture into the dungeon, enter the first room or advance to the next room.)
Create Undead — Whenever you complete a dungeon, return target creature card from your graveyard to the battlefield.

Tomb of Horrors Adventurer

When Tomb of Horrors Adventurer enters the battlefield, you take the initiative.
Whenever you cast your second spell each turn, copy it. If you've completed a dungeon, copy that spell twice instead. You may choose new targets for the copies. (A copy of a permanent spell becomes a token.)

Vicious Battlerager

When Vicious Battlerager enters the battlefield, you take the initiative.
Spiked Retribution — Whenever Vicious Battlerager becomes blocked by a creature, that creature's controller loses 5 life.

Aarakocra Sneak

Flying
When Aarakocra Sneak enters the battlefield, you take the initiative.

Rilsa Rael, Kingpin

Deathtouch
When Rilsa Rael, Kingpin enters the battlefield, you take the initiative.
Whenever you attack, target attacking creature gains deathtouch until end of turn. If you've completed a dungeon, that creature also gets +5/+0 and gains first strike and menace until end of turn.

Passageway Seer

Lifelink
When Passageway Seer enters the battlefield, you take the initiative.
At the beginning of your end step, if you have the initiative, put a +1/+1 counter on Passageway Seer.

Goliath Paladin

Vigilance
When Goliath Paladin enters the battlefield, you take the initiative.

Feywild Caretaker

When Feywild Caretaker enters the battlefield, you take the initiative.
At the beginning of your end step, if you have the initiative, create a 1/1 blue Faerie Dragon creature token with flying.