Sub-domain mapping from a different host

Hi all, my question is, if its possible to map subdomains from other different host just by changing the DNS record A or CNAME from the other host?

The client is using a website provided by a local political institution, and they are a regional institution which they use a subdomain of a local city provided by the main political institution. Also there is no way of them using a main domain name which would make this a regular and normal process but thats out of question :slight_smile: