...and I'd like to find out if it's possble to take that computer off my account so I can use the remaining 3 months of my CCleaner sub on my new laptop.
TIA for any advice.
Paul
To get you started you should just be able to use your existing licence/key to register CCleaner on your new machine.
You should then contact support and tell them what has happened.
They will take the necessary steps.
They may issue a new key and cancel the old key if you/they feel that is needed.
The contact form is here, Please only send one, note the ticket number, and be patient, it can take them a long time to reply at the moment. (week? longer?)
But if you activate it with your existing key then your CCleaner Pro should be working on the new machine whilst you are waiting.
<a href="https://support.ccleaner.com/s/contact-form?language=en_US&form=general" ipsnoembed="true" rel="external nofollow">https://support.ccleaner.com/s/contact-form?language=en_US&form=general</a>