Garrulous Sycophant

The last ability of Garrulous Sycophant checks to see if you're the monarch as your end step 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 end step 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.

Being the monarch carries two inherent triggered abilities. "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."

Abilities that trigger whenever you "become the monarch" trigger only if you aren't already the monarch. For example, if you are already the monarch as Custodi Lich enters the battlefield, its last ability won't trigger.