What will the club do at the school festival next month?

1. It will perform at the school festival.
2. They will perform at the school festival.
[Which answer is correct? Do we have to use 'it' or 'they' in this case?]

You'd have better answers if you used more detail. Remember -- "club" is singular, "club members" is plural. Here are some examples:

What will the Polynesian Club do at the school festival next month?
- A few members will perform traditional dances.
- Some members will provide the music needed for others to perform traditional dances.

What will the Computer Club do at the school festival next month?
- Members will demonstrate how to write code that makes the robots do tricks.
- It will have posters with binary code on them, as well as demonstrations of different computer tools and programs, such as XD cards, gaming programs, and photo enhancements.

Thank you for your kind explanation.

Do you mean we can use both #1 and #2?
If all the club members perform, do we have to say,"They will perform..."
Or do we have to say, "It will perform..." because the club is singular?

Use "club" when you mean the entire club (not individual members) and use a singular verb with it.

Use "club members" or just "members" or "member" when referring to individuals.

"They will perform" = all or some of the members will be taking part in demonstrating, dancing, or whatever is going on.

"It will have a booth" = the club as a whole, not meaning any members individually.

In this case, both "it" and "they" can be used, depending on the context.

If the club is a single entity or if you are referring to the club as a whole, you can use "it". For example: "The Math Club will perform at the school festival. It will showcase its mathematical talents."

If you are referring to the members of the club as individuals or if you want to emphasize the plural nature of the club members, you can use "they". For example: "The Chess Club will perform at the school festival. They will demonstrate their strategic skills."

So, both "It will perform at the school festival" and "They will perform at the school festival" are correct, but they convey slightly different nuances and perspectives.