Previewing an website that was temporarily moved on a new hosting accout can be made by configuring your computer to point to thew IP address.
Even if the DNS service was not configured to point to the new IP address, your PC can be configured to send the request to the new IP. This is how you will have access to your website hosted on the new account, and in the meantime, the rest of the visitor will see the website hosted on the old account.
If you are using Windows as an operating systam, you will have to eddit the file c:\Windows\System32\drivers\etc\hosts (you will need administrator rights). The path may differ if you have windows installed on other partition than c:\
In this file you will have to add two lines, like in the example shown below:
*220.127.116.11 is the IP of your new hosting account and domain.tld is your domain name.
You can find the IP of your hosting account in cPanel, in the section "Server Information" -> Shared IP.
After you made these changes, you will have to restart your browser.
Don't forget to delete these two lines after you finished the tests.