this will be the first

[curious]

1- This will be the first time that he is giving a concert in the US.

2- This will be the first time that he gives a concert in the US.

3- This will be the first time that he will give a concert in the US.

4- This will be the first time that he will be giving a concert in the US.

5- This will be the first time that he will have given a concert in the US.

6- This will be the first time that he has given a concert in the US.

Which ones are correct?

[Johan[@CLT]]

1- This will be the first time that he is giving a concert in the US.
2- This will be the first time that he gives a concert in the US.
3- This will be the first time that he will give a concert in the US.
4- This will be the first time that he will be giving a concert in the US.
5- This will be the first time that he will have given a concert in the US.
6- This will be the first time that he has given a concert in the US.
Which ones are correct?

Numbers 5 & 6 sound very strange here, when using "will" you indicate the simple future and in the next part of the sentence you use the present perfect form.
Present perfect is used for an action that started in the past but when there is a link with the now.
Number 2 The use of the simple present in the second part of the sentence doesn't look right to me. Simple present is used to indicate habits for example: I work every day from 8am till 4pm. Due to it will be his first concert in the US.
The same for number 1 That's the present continuous.
I think that number 4 is a correct way to say this.
I should say: This will be the first time that he is going to give a concert in the US.
Eager to know what others have to say about this.
Kind Regards

[curious]

me too.

[Johan[@CLT]]

I should go for a safe solution here. If you can of course, it can be a really frustrating from time to time It's not always plain sailing.

Kind Regards