how to download safari after software update

Are you unable to find the Safari app? Safari is already incorporated in macOS and is unavailable as a separate download.

Safari is installed in your Mac's Applications folder. To navigate to it, Go > Applications from the Finder, or simply perform a Spotlight search for Safari.

To keep Safari in the Dock, drag its app icon in the Dock to some other location in the Dock, where it will remain even if you were to quit Safari.

Use the Dock on Mac - Apple Support