How to test another theme in a live WordPress website instead of live preview?

To try new theme over live wordpress site you need to duplicate the site in staging. There are many ways to do that:

  • Manually: create a sub-domain (ex: staging.domain.com) copy files and DB there and do your changes there after tested well migrate them to live.
  • Using plugin: A plugin named WP-Staging may help you the manual process.
  • You can use wp-engine service, which help you manage staging things.

Hope one of the above way be helpful for you. A help link to check.