Angelic Arbiter's last ability applies if an opponent attacked with at least one creature during the current turn.

If Angelic Arbiter enters during an opponent's turn, its abilities take actions that player performed earlier in the turn into account, even though it wasn't on the battlefield at the time. For example, if an opponent casts a spell, then you use Leyline of Anticipation's ability to cast Angelic Arbiter as though it had flash, that player won't be able to attack with creatures that turn.

During your turn, Angelic Arbiter's abilities have no effect on the game.

If Angelic Arbiter leaves the battlefield during an opponent's turn, its abilities cease to affect the game. For example, if an opponent casts Doom Blade to destroy Angelic Arbiter, that player may then attack with creatures.

During an opponent's turn, that opponent may either cast spells or attack with creatures, but not both (assuming that Angelic Arbiter is on the battlefield for the entirety of that turn). The player may perform other actions, such as activating abilities and playing lands.