How to migrate new site to an existing plan?

I have a LIVE site with Site plan: CMS.
I have another Site plan: Starter

I redid the design on the Starter plan with a new template in hopes of replacing the CMS one… How do I swap them to make the Starter the CMS plan so the new template is live.

IS there a way to make my new site live easily??

Here is my site Read-Only: LINK
(how to share your site Read-Only link)