First you have to contact your other host with a request to change the A record for the subdomain in question. The A records has to be pointed to your server's shared IP address. You can find your server's shared IP from your Customers' Area --> My Account --> Manage (next to the account you are interested in).

Finally you have to set your account to work by the external subdomain. For this purpose apply it as a primary domain name for your account. This can be done from your Customer's Area --> Get Support --> Report a hosting related issue --> Domain name change.

Alternatively you can use a CNAME record for the external subdomain and point it to a subdomain on your current account.