It's possible to setup a reverse proxy using Apache to establish a subdirectory on Ghost(Pro).

For this configuration to work successfully, you must be on a Business plan with a subdirectory enabled via support@ghost.org. You must also paste the exact configuration below into your apache configuration file, updating each line as specified so that it meets our reverse proxy rules.

The below configuration has been tested and works with these exact settings if there are no conflicting top-level config issues.
# You'll need to enable the ssl, proxy and proxy_http modules:
# sudo a2enmod ssl proxy proxy_http

<VirtualHost *:80>
        ServerName <yourdomain.com>; # Replace with your domain
        Redirect permanent / https://<yourdomain.com>  # Replace with your domain
</VirtualHost>
<VirtualHost *:443>
	ServerName <yourdomain.com>; # Replace with your domain
        
        SSLProxyEngine on

        # Your SSL Certificate details. Replace with your own SSL setup
	# SSLCertificateFile /path/to/cert
	# SSLCertificateKeyFile /path/to/key;

        <Location "/blog">
                # Replace with your subdomain, https matters here
        	ProxyPass https://<yoursubdomain>.ghost.io/blog/
	        ProxyPassReverse https://<yoursubdomain>.ghost.io/blog/ 
        </Location>
</VirtualHost>