Containment Priest

• WOTC Official Reminder Textofficial rules
  Flash — You may cast this spell any time you could cast an instant.

• WWizards of the Coast2021-03-19
  Official Ruling
  If Containment Priest enters the battlefield without being cast, its ability won't exile itself.
• WWizards of the Coast2021-03-19
  Official Ruling
  Containment Priest's last ability won't affect any creatures that were cast, including ones cast from unusual zones such as your graveyard.
• WWizards of the Coast2021-03-19
  Official Ruling
  If Containment Priest enters the battlefield at the same time as other creatures, its ability won't affect those creatures.
• WWizards of the Coast2021-03-19
  Official Ruling
  If a noncreature card wasn't cast and is entering the battlefield as a creature (due to an effect such as that of March of the Machines), it will be exiled. Conversely, if a creature card wasn't cast and is entering the battlefield as a noncreature permanent (for example, Heliod, Sun-Crowned with insufficient devotion), it won't be exiled.

Rulings via Scryfall