Subscription

Canceling a subscription does NOT Cancel your Adobe User Account and or Adobe ID. 

If for some reason you want to purchase another subscription, for a different program, group of programs, photography plan, or All Apps (Full Subscription) you do that at the main Adobe website and use your original Adobe ID.

Nothing is stopping you from canceling one subscription and purchasing another with the same Adobe ID.

Now IF you Actually Canceled, Delete, your Adobe ID, which you can do, then that ID is gone and can not be reactivated as far as I know. you then need to create a New Adobe ID.

So what was it exactly that you canceled and or deleted?

I don't know what you mean by "old account."  You either have an active subscription plan or you don't.   Log-in to your adobe account below to confirm your account status is what you think it should be. 

https://account.adobe.com/plans

If you're asking us how to activate legacy Creative Suite software, we need more information.  Which version?  Which operating system do you have?

IMPORTANT FOR MAC USERS:

Creative Suite software won't run on mac OS Catalina.  

CS1, CS2 and CS3 are dead.  Adobe disabled the activatuion servers years ago and officially ended all support. 

This is a public forum, not the link to Adobe support
-other users here can't help with an account problem
Be sure to remain signed in with your Adobe ID before accessing the link below
-you must also allow 'cookies' in your web browser for this to work
https://helpx.adobe.com/contact/support.html

Also - beware of answering anyone who sends you a private message
https://community.adobe.com/t5/community-help/avoid-phishing-3-easy-ways-to-identify-adobe-staff/td-p/10791730