Help getting Adobe on Same computer, new drive

As noted you can point the install location to another location, but given that you are updating a Mac, this is likely an external drive and not a replacement for the original disk as Macs come with an internal SSD that is not upgradeable by users.  I would recommend doing a search on these forums for issues users have come across and consider keeping your installations of the apps on the primary HDD and storing files on the external SSD.

If I get your question right. This will help you

https://helpx.adobe.com/download-install/using/change-install-location.html

When you have a subscription
-sign in to your account with your ID and password
-Cloud Manager to install all programs https://www.adobe.com/ie/creativecloud/desktop-app.html
-https://community.adobe.com/t5/get-started/how-to-activate-your-adobe-software/td-p/9636861?page=1