How Do I Uninstall a Current WordPress Theme and Install a Fresh Theme

You can install the new theme and preview how it would look before changing it. See https://en.support.wordpress.com/themes/#preview-themes for more info.

Once you have tested that it works, you can then activate the new theme. I would keep the old theme for a few weeks until you're confident that there is nothing else needed, then take a backup of old theme before deleting it.

I'd also review the current theme's functions.php file for any customised code that you may want to copy in to the new theme's functions.php file or write a plugin to make it compatible across all themes.

As a final note though in case not obvious - install the new theme first before deleting the current/active theme.

Themes are quite often depending on certain plugins, such as Custom Fields or Custom Post Type, to control and display the contents. If you install a different theme the chance is that it doesn't work the same way. Start inactivating modules one-by-one and see how/if the site works.

All theme files are located in the wp-content/themes-folder. If you remove it there should be no remnants, unless some bad practices are present:

• Hacks have been made to the WP core files to suit the theme
• Hacks have been made to the any plugin files to suit the theme
• Files in the media library have been used in the theme

You could always use the theme live preview function to test new themes without actually going live with it.

There is more ways to do it, like cpanel or ftp access, check out codex page https://codex.wordpress.org/Using_Themes