I have the new mac desktop... But my adobe suite is on my old laptop

Short answer: NO.  That would be a violation of Adobe's End User License Agreement. 

Technically you own nothing.  The former laptop owner should have wiped the hard disk before handing it to you.  The fact that he/she didn't means you're using Adobe software illegally.

Pre-Creative Cloud software won't run much less install on modern Macs.  So even if you had purchased a legitimate license and installation disks when they were still being sold, they would be useless on Catalina & Big Sur. 

Creative Suite is no longer legally sold by any vendor, retailer or country.

MODERN OPTIONS:
Photoshop Elements or Premier Elements (approx $100, no subscription needed)
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan -- approx $10/month for 12 months. Includes the very latest versions of these great products & services:
-- Photoshop CC and Photoshop on iPad
-- Lightroom on desktop, mobile and the web
-- Lightroom Classic
-- Portfolio website + hosting
-- Spark with premium features
-- Bridge
-- 20 GB cloud storage (upgradable to 1 TB).
https://www.adobe.com/creativecloud/photography.html

Creative Cloud All Apps (31 + apps & services) and Single Apps Plans
https://www.adobe.com/creativecloud/plans.html

No... you do not own the programs, and the original ower was supposed to DE-activate before selling the computer

Also, CS6 and earlier will not work on a Mac with the M1 processor OR with Apple's BS operating system

Transfer (selling or giving your software away) https://helpx.adobe.com/x-productkb/policy-pricing/transfer-product-license.html
-you may NOT sell or transfer an Education serial number

Unless the person who sold you the Macbook also transferred the license for the Creative Suite (I'm assuming it's the Creative Suite, since Creative Cloud is subscription only), then you have been using that software illegally. You will need to contact them to transfer the license and to acquire the installation media and license number.

See here for information on how to get a license transferred: https://helpx.adobe.com/x-productkb/policy-pricing/transfer-product-license.html

Also, be aware that Mac OSes from, I think, Catalina onward will NOT run the Creative Suite software. Catalina onward runs only 64-bit applications, and Creative Suite is 32-bit.