The Ancient One

Descend 8 — The Ancient One can't attack or block unless there are eight or more permanent cards in your graveyard.
{2}{U}{B}: Draw a card, then discard a card. When you discard a card this way, target player mills cards equal to its mana value.

The Lost Caverns of Ixalan

The Lost Caverns of Ixalan Promos

Cards with the ability word "descend N" have abilities that care if you have at least N permanent cards in your graveyard.

Once The Ancient One has legally attacked or blocked, removing permanent cards from your graveyard so the descend 8 ability no longer applies won't remove The Ancient One from combat.

Some descend triggered abilities include intervening "if" clauses (i.e. "if you have [four or eight] permanent cards in your graveyard" in the middle of the ability). Each of these abilities checks your graveyard at the moment it would trigger to see if it does. If you don't have the required number of permanent cards in your graveyard at that time, the ability doesn't trigger at all. If it does trigger, it will check again as it tries to resolve. If you don't have the required number of permanent cards in your graveyard at that time, the ability won't resolve and none of its effects will happen.

You don't choose a target for The Ancient One's activated ability at the time you activate it. Rather, a second "reflexive" ability triggers when you discard a card this way. You choose a target for that ability as it goes on the stack. Each player may respond to this triggered ability as normal.