What should I word should I put there their and they're in the sentence unless there is some kind of delay zuri Ross Will finish her project tonight

The correct word to use here is indeed "there":

Unless there is some kind of delay, Zuri Ross will finish her project tonight.

Explanation:

The three words "there", "their", and "they're" are pronounced in exactly the same way, which can be confusing when we need to write them down. But there is a simple way to distinguish them:

1. they're → is the contraction of two words: They are. "They're" is used as the subject as well as the verb of a sentence. For example: They're already here! / They're talking about you.

2. their → is the possessive pronoun for the third person plural. It is used to show that something belongs to someone. For example: I saw their new car, it is really nice. / Their mother is looking for them.

3. there → this word can be used to refer to a location, almost opposite to "here". But it is also employed in "there + to be" to indicate the existence of something. For example: There is a park near here. / There was delay, so they haven't arrive yet.