When a form is completed, how do I get a new blank form to appear?

You can set your Thank you page to redirect to a new form, here is a guide on how to do that:

https://www.jotform.com/help/211-Setting-Up-the-Thank-You-Page

You can use a Redirect to external link option and put there the URL of the other form.

Let us know if you have any further questions.

Thank you!