Old/New computer

Yes, assuming your old computer supports Creative Cloud system requirements.

Make sure your computer meets the CPU & GPU requirements. Most Creative Cloud apps work on:

• Windows 11 (64-bit), Windows 10 versions 21H2, 21H1, 20H2, 2004, and 1909 (LTSB branches are not supported;)
• macOS 12 (Monterey), macOS 11 (Big Sur), macOS 10.16 or 10.15 (Catalina).

- https://helpx.adobe.com/creative-cloud/system-requirements.html

Cloud License allows 2 activations at a time http://www.adobe.com/legal/licenses-terms.html
-you may use on ONE computer at a time, and you may NOT share your subscription
-https://community.adobe.com/t5/download-install/on-how-many-computers-can-i-use-my-creative-cloud-subscription/td-p/11233565?cid=101&cgid=18323&page=1
-Install on a 2nd computer https://community.adobe.com/t5/Get-Started/Installing-creative-cloud-on-two-devices/td-p/6048133
-https://helpx.adobe.com/creative-cloud/help/sign-in-out-activate-apps.html
-Windows or Mac does not matter... 2 on the same operating system, or 1 on each

I've moved this from the Using the Community forum (which is the forum for issues using the forums) to the Download and install forum.

Yes. Download the CC app and install from there:

https://helpx.adobe.com/download-install/kb/creative-cloud-desktop-app-download.html