Upgrade to High Sierra on iMac

If you select About This Mac in the Apple () menu, what does it tell you about the model and hardware model year (or time of year) of your iMac?

• If your 21.5" iMac is from Late 2009 through Late 2011, High Sierra is the end of the line.
• If it is from Late 2012 through Late 2013, Catalina is the end of the line.
• If it is from Mid 2014, Big Sur is the end of the line.
• If it is from Late 2015, Monterey is the end of the line.
• If it is from 2017, Ventura is the end of the line.
• It cannot be the one from 2019, as that one cannot run anything earlier than Mojave.

Best case is that you have one of the 21.5" 2017 iMacs – since Ventura is one of the "most recent three" versions of macOS that is supported by vendors like Adobe and Microsoft, and probably will be for close to a year longer.

How to download and install macOS - Apple Support

If you upgrade to Catalina or later,

• 32-bit applications will stop working
• iTunes will go away, replaced by separate applications (Music, TV, Podcasts, Books) and the Finder
• You will be able to run current versions of FireFox, LibreOffice, GIMP, and the commercial Affinity V2 programs – Photo, Designer, Publisher.

That depends on the year model of your iMac. see > Identify your iMac model - Apple Support

Note that the "Newest compatible operating system" is listed for each model.

If your iMac qualifies for an upgrade. see > Update macOS on Mac - Apple Support

If you have a 2009, 2010 or 2011 iMac it could well be that High Sierra is end of the line

Go to the App Store>software update or to system preferences>software update

If it is stating "your Mac is up to date" then it is end of the line and you cannot update any further