Learn German: Ich habe nicht genug Zeit, bevor das Stück anfängt. - I do not have enough time before the play begins.

bevor (before) is a subordinating conjunction. This means it creates a dependent clause and pushes the conjugated verb all the way to the end of that clause.

Isn't anfangen a separable verb? Why isn't it split up here?

Yes, anfangen (to begin) is a separable verb. In a normal main clause, it splits (like Das Stück fängt an). But in a subordinate clause introduced by bevor, the verb is pushed to the end. When a separable verb is forced to the end of a clause like this, its prefix (an-) and verb stem (-fängt) stay glued together as one single word: anfängt.

Why does das Stück mean "the play"? I thought it meant "piece".

You're right, das Stück literally means "the piece". However, it is also the standard German word for a theater play, which is short for das Theaterstück.

Why is nicht placed right before genug Zeit?

When negating a specific idea or noun phrase in a sentence, nicht usually goes right in front of that element. Here, it directly negates genug Zeit to mean "not enough time".