I have a late 2013, 27" iMac with Catalina version 10.15.7. Can this be used as an external monitor if connected to a current Apple Macbook Air. If the operating system is a factor can it be changed to High Sierra?
Earlier displays & monitors
No.
Review the document: Use your iMac as a display with target display mode - Apple Support
Target display mode is a feature available with late 2009-Mid 2014 iMacs. The display Mac has to be running macOS High Sierra or older and the signal producing Mac has to be running macOS Catalina (ca. 2019) or earlier.
Using an external monitor
