First I just want to be clear about what you're asking...
People call fred.domain.com a "subdomain" but most of the time it's actually a
hostname
You can point the IP of fred.domain.com at anything you like - including another host. That's the A record only though, eg what it would connect to if you tried to load
http://fred.domain.com/
If you truly want to delegate a subdomain, that is being able to control the subdomain fred.domain.com, and add/maintain records like blah.fred.domain.com and haha.fred.domain.com then that gets more complicated.