No. Each Rize Trade account can use the free trial only once. Checkout does not grant a second full trial after you have already started one.
Why a second trial is not available
When you start a free trial, your account is marked as having used the trial. Checkout only applies a trial if that mark is not already set. There is no in-app reset that clears it.
What you can do instead
If your trial is still active and you need more time, that is a different path. See Can I get a trial extension?.
After a trial has been used, choose a paid plan when you are ready, or stay on the free tier with its limits. For how the trial works, see How the 7-day free trial works.