Regal Sliver

If the triggered ability that causes the monarch to draw a card goes on the stack and a different player becomes the monarch before that ability resolves, the first player will still draw the card.

If the monarch leaves the game during another player's turn, that player becomes the monarch. If the monarch leaves the game during their turn, the next player in turn order becomes the monarch.

There are two inherent triggered abilities associated with being the monarch. These triggered abilities have no source and are controlled by the player who was the monarch at the time the abilities triggered. The full texts of these abilities are "At the beginning of the monarch's end step, that player draws a card" and "Whenever a creature deals combat damage to the monarch, its controller becomes the monarch."