It appears that you understand that installing a newer operating system also installs the latest version of Safari and your question is how can Safari be updated when the OS can not be upgraded? First, whether your OS can be upgraded depends on which OS you have installed and what year and model Mac you have. An update does not install a newer OS. It merely installs the latest version of the same OS that you have. You can check for available upgrades in the Apple App Store. Also, if you cannot upgrade, then you might consider installing another browser such as Firefox or one of the many browsers available in the App Store. They can be individually upgraded as needed.