Is it possible to redirect a DNS to a different server in Apache?

Let's say a DNS named system.example.com is redirected to my server IP where I have Apache installed in it. Let's also say the domain example.com was bought in GoDaddy and I have no admin control over this DNS, so that means I can't just redirect system.example.com to a different server in GoDaddy.

I'd like to create a new redirection with Apache to a server with a different IP address. In pseudocode, I think about something like:

<VirtualHost *:80>
    ServerName system.example.com
    Redirect 301 / http://192.0.2.1/
</VirtualHost>

This apache config doesn't work, it's just a sample. The idea is to redirect the domain that is arriving on my server to a different server. That would be exactly the same as using the A redirection in GoDaddy... But doing it in Apache instead. Is it possible? Can I redirect a DNS that is arriving on my server to a different server?

If I correctly understood what you are asking about, no. The name resolution is completely controlled on the client side, the only thing you can do is to update DNS RRs on the server. So ask somebody who can control DNS. We're solving business problems here, and this is normal to ask people to do actions for the business sake.

You can use raw IP address in HTTP addresses, so the redirection you suggested will work. However, this is not recommended nowadays to use IP addresses in this context. Better use any other domain that you can control. This is what you are essentially doing anyway.

Yes and no.

No, you can't "redirect DNS" with a web server. If the hostname system.example.com needs to resolve to a different server then you need to adjust the DNS record. (You can't use the HTTP protocol to make changes at the level of the DNS protocol.)

Yes, you can configure your webserver so that HTTP requests (either all or only those for a particular hostname) are answered with a HTTP redirect.
A redirect instructs a web browser to make a new request to a different location and the visitor to your website will see that in the address bar of their browser http://system.example.com is changed to http://192.0.2.1/.

More common when you want a web server on system.example.com to show content from a different web server is by configuring it as "reverse proxy" rather than by sending a redirect. That leaves the address bar unchanged but may cause other issues and will cost you a lot more bandwidth.