My iMac was recently updated. As a result I have lost my Microsoft applications that worked prior to the update. I'd like them back.

If you were running Office 2011 or earlier, and have updated to macOS Catalina or Big Sur, you will have to purchase a newer version of Office, find an alternative, or downgrade your Mac to the previous version of macOS you were running.

Office 2011 and earlier and 32 bit applications and are not compatible with Catalina or Big Sur.

Microsoft no longer supports any version of Office older than Office 2019.

Office 2016 when fully updated, was the first version of Office compatible with Catalina.

You probably have an older Office-version (32-bit) that is not compatible with BigSur (or Catalina).

If that's the case, you'll have to pay for an upgrade, e.g. to Microsoft 365 or download and install a free alternative like LibreOffice for Mac or use Apple's Pages, Numbers and Keynote (these apps are already on your Mac)