Access files at new location using old file paths

I believe I’ve found the solution. I add the following

RewriteRule ^example_directory/files/(.*) new_directory/$1

to my WordPress .htaccess rules like so:

RewriteEngine On
RewriteBase /
RewriteRule ^example_directory/files/(.*) new_directory/$1
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]

I couldn’t get it working before and I think the key was moving the new RewriteRule directive to the line directly following RewriteBase /