I get the message that 'TurboTax is already running under another account.' This is probably my previous session. How can I clear this condition?

To resolve this, make sure all your internet tabs are closed.  Next, I  suggest clearing your cookies and cache to (How to clear your cache).  

Alternatively, you can also try to use incognito mode (Ctrl + shift + N in Chrome and Edge browsers) , log into your return, and try again.