If the CC that you have is a seat of the CC for Team of your old organization, then you need to get the seat unassigned . it can be done by deactivating it Activation & Deactivation Help, the program admin
The seat is then unassigned by the program Admin by revoking the invite.
If the CC that you have is CC for individual then also it needs to deactivated .
Next you need to sign back in to CC desktop App with the new Adobe ID(applicable to both type of CC)
You do not need to uninstall.