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://account.parallels.com/.
Switch to Parallels Access > Settings and switch to the account with the Parallels Access subscription you would like to use.
Now Parallels Access will see your subscription and connect you to the remote computer.