1. Login to https://portal.ultradns.com
2. Create the subdomain as a primary domain in UltraDNS.
3. Add desired records to the subdomain in UltraDNS.
4. Contact the other DNS provider to determine how to add NS records on their name servers.
You will need to add NS Records with the subdomain's name as the host name in the apex domain's zone file pointing to your UltraDNS Name Servers.