Learn Russian: Нужно предупредить клиентов за неделю до премьеры. - It is necessary to warn the clients a week before the premiere.

This is the standard Russian formula for saying how much time passes before an event. You use за plus the amount of time in the Accusative case (неделю), followed by до plus the event in the Genitive case (премьеры).

Why is the word for week in the Accusative case (неделю)?

In this specific за ... до time construction, the preposition за always requires the amount of time to be in the Accusative case. Because неделя (week) is a feminine noun, its ending changes to -ю.

Why does the direct object клиентов look like it is in the Genitive case?

It is actually in the Accusative plural, since the clients are the direct object of the verb предупредить (to warn). Remember that for animate nouns (living things like people and animals) in the plural, the Accusative form is identical to the Genitive form.

Why use the perfective verb предупредить instead of the imperfective предупреждать?

We use the perfective aspect here because this is a single, specific action that needs to be successfully completed for this particular premiere. If it were a general rule or habit, like 'one must always warn clients,' you would use the imperfective предупреждать.