How do I disable my own webhosting space using my own cPanel?

So I recently moved host, but my old webhost still has the relevant data and databases.

Unfortunately the old webhost contains a Wordpress installation (using Updraftplus) that is running automatic backups to my Google Drive. It is doing it even after I changed the main domain's namesevers to point to the new webhost.

Is there a way for me to disable the site at the old webhost using my own cPanel?

Thanks for the help!