Keeper of Keys

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.

The last ability of Keeper of Keys checks to see if you're the monarch as your upkeep begins. If you're not, the ability won't trigger at all. You won't be able to do anything that would make you the monarch during your upkeep in time to have that ability trigger. The ability will also check to see if you're the monarch as it tries to resolve. If you're not the monarch at that time, the ability will have no effect.