I have an active Parallels Access subscription, but when I'm trying to connect to a remote computer, Parallels Access suggests to buy a new one.
A Parallels account allows to combine a private and several business accounts under one email address. Parallels Access uses a wrong account to connect you to a remote computer.
Log in to your Parallels account at https://my.parallels.com/.
Click on cog-wheel button next to Parallels Access icon
Switch Use Parallels Access licenses that belong to to Business Account.
Now Parallels Access will see your Business subscription and connect you to the remote computer.