Even before Paramount+ supplanted CBS All Access in March, ViacomCBS mentioned that the $10 per month streaming service would add a new cheaper option in June. Now that June is here, Android Police and Tom's Hardware point out this FAQ live on the Paramount+ site that explains the new Essential plan will be available starting on June 7th.
The existing cheaper option with "Limited Commercials" for $6 per month will go away, so if you'd like to subscribe to it then you will need to sign up before the 7th. One reason you might want to do that is that unlike the new Essential plan, it includes access to live broadcasts from your local CBS station, and as long as your subscription remains active, you'll continue to stay on it.
Otherwise, the new $5 per month or $50 per year Essential Plan promises the following:
Stream with limited commercial interruptions
Watch 30,000+ episodes, movies & originals on demand
Stream NFL on CBS and Champions League live
Get 24/7 national news with CBSN
On the other hand, the more expensive version is still available for $10 per month or $100 per year that allows users to download content for offline viewing, and (with exceptions for some shows and live broadcasts) no advertisements.