I originally installed CiviCRM in Wordpress on our regular website. I am now wanting to uncomplicate that website by moving our CiviCRM installation to another subdomain so it can be used separately from our main website in a second Wordpress installation. I haven't been able to find a recommended procedure for our specific use case.
Note: CiviCRM is installed in a separate database from Wordpress already. The new subdomain is currently empty.
Edit, clarification, and question based on the answer below:
We do have links to the newsletter subscription form. And we have the admin utilities plugin installed. I also have some custom roles created.
I am planning to run Wordpress in the subdomain using the same host as the current site, so the CiviCRM database itself doesn't necessarily have to move.
I was wondering if it would be possible to simply disable the civicrm plugin, copy the existing website over to the new location, duplicating the database for wordpress, but using the existing database for CiviCRM. Perform whatever find/replace was necessary to change domain.com to new.domain.com, and then re-enable CiviCRM? If that could work, I'd just need some idea of what find/replace would be necessary.