Can I update Safari to 14.1.2 on my old iMac 27" running macOS High Sierra?

Back up your data, check the application compatibility table, click here, and if your iMac is a 2012 or newer model, then on the download link for a higher OS. Alternatively, use a different web browser as needed.

Catalina and above won't run 32-bit software and split the functions of iTunes up; if you choose one of them, use Go64 as well.

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No. Safari 14, requires macOS Catalina or Mojave at least. It is not compatible with High Sierra.