Where did this plug in come from?
If it is still using mysql it must be very outdated.
No one should still be using mysql any more, it is obsolete and has been removed in PHP 7 and was deprecated in version 5.x.
What version of PHP is the server running? I’m guessing it will be 7 to get that error.
That plug in should be removed or updated.
This usually occurs when you go from an old version of PHP to a new version of PHP.
Old versions of PHP use mysql_*() API functions. These have been deprecated/retired for years now.
PHP-7.0 + PHP-7.1 have finally completely removed this code.
To resolve this, update your WordPress core + theme + plugins.
If problem persists, then enable WP_DEBUG in your wp-config.php file + you’ll get the exact line throwing the PHP Fatal.
If your Theme has the problem, you’re using a Theme which has been abandoned + you’ll have to change to a new Theme.
If any plugins show this problem, just disable them.
Since this type of error usually breaks the admin panel, you can disable plugins manually with FTP.
I normally do this for clients by creating wp-content/plugins-aside + moving the plugin directory causing Fatal from plugins to plugins-aside.
Once you’ve logged in, you can determine how to correct plugin problem, which will likely be replacing the plugin, as this type of problem usually means the plugin has been abandoned.