Priority sets the order in which monster effects and trap cards can be activated. Any monster with an Ignition Effect (Cost Effect) has priority over cards like Trap Hole, Torrential Tribute, Bottomless Trap Hole, Compulsory Evacuation Device, etc…
Player A Tribute Summons Mobius the Frost Monarch and chooses the 2 Spell/Trap cards to destroy
Player B activates Trap Hole.
Even though Mobius is destroyed, he was still summoned and gets his effect (This is a Trigger Effect)
Player A Special Summons Black Luster Soldier- Envoy of the Beginning
Player B activates Bottomless Trap Hole
Player A says “I was going to remove that monster from play”
Since Envoy has an Ignition Effect, the turn player gets priority over Player B’s Bottomless Trap Hole. The monster is removed from play, and Envoy is destroyed and removed from play by Bottomless.
Player A Normal Summons Breaker the Magical Warrior
Player B activates Trap Hole
Since Trap Hole is chained to placing the Spell Counter on Breaker, Trap Hole resolves before the counter is placed
A small list of a few monsters with priority
Lady Ninja Yae