Please proceed with the following steps :
1. Login to your Cpanel
2. Create a full Backup of the domain via the cpanel.
3. Upload this backup, which will be in the .tar.gz format to the new hosting server you have purchased.
If you have the root password to the new server ( if VPS) you can restore the full backup using your WHM, there would be the restore full backup feature provided.
If you do not have the root password, and you are just a reseller, you can let your support know to ask them to restore it for you.
Or follow the simplest method : Let your new remote support know the cpanel username , password and domainname on your old host, they will create the backup, copy to new server and restore it for you.