I’d suggest to rename the repository, and avoid creating a new clone of it.
Why? GitHub is very smart: when you rename a repository, every web and git request that use the old URL will be automatically redirected to the new one.
For example, I renamed https://github.com/mlocati/login_destination to https://github.com/concrete5-community/login_destination (see How to move a GitHub repository to the concrete5-community organization - YouTube to see how I did it).
If you visit the old URL with the browser, you’ll be automatically redirected to the new one.
And even git clone https://github.com/mlocati/login_destination.git still works.