I am quite inexperienced with DNS, so this might be simple.
Our main domain foo.com is hosted at provider A. Now, we would like to host bar.foo.com at some other provider B - they have the domain set up with them, so I figure that I can do this by somehow adding the nameserver at provider B to the DNS configuration at provider A.
The current DNS config is as follows: https://i.stack.imgur.com/2myDE.png
How can I add the new subdomain to this configuration?
Note: maybe shared hosting provider is a more accurate term. Provider B is discountasp.net - I know their nameserver adresses, just not sure how to add them to my original setup.