Hello

which existing calendar? from which tool?

usually, you can import existing calendar by exporting it from the 'original' account/location and then importing it to Outlook 2010

if original location was an Outlook calendar, you have to export existing calendar to a PST file and then import it to your new Outlook profile set by Office 365

The pst file has been exported from my Outlook 2003, but there is nothing apparent within Outlook 365 which indicates the ability to either import (or export)  capability, just blank calendar screens.

Hi,

You can import the .pst file into Outlook itself, not directly in the Calendar.  You can do this by clicking on the File menu, then selecting Open, Import, and completing the resulting Import/Export as appropriate.  

You can also read about using .pst files at support.microsoft.com/.../287070.

Perhaps this is where I am failing. I see absolutely no ribbons, tabs or anything approximating the usual File, Edit, etc. at the top of my 365 screen. It appears to just be a clean calendar screen. Thus, there is no visible process to accomplish the usual Import/Export process.

Are you accessing your calendar through the Outlook desktop program or the Web App? The import must be done through the desktop client.