Newer versions of Safari are only offered within a supported macOS operating system upgrade, or if supported, via security updates. Your macOS High Sierra (10.13.6) fell off the Apple supported operating systems rotation in Fall 2020, so no Safari updates are available without upgrading the operating system itself.
Your options are to switch to the current Firefox 93, Chrome browser (94), or the Brave browser to get current security protocols that would satisfy your financial institution, while remaining on High Sierra. Or, If you want to stick with Safari, that will require an upgrade to a newer version of macOS, and that is dictated by the age of your Mac hardware.
If you want to upgrade, then using strictly Safari, visit How to get old versions of macOS, where you can determine which version you can upgrade to based on you meeting the hardware requirements. Then follow that corresponding macOS link to the Mac App Store for the full installer download. If you have 32-bit applications that you are dependent, and there are no 64-bit replacements by their vendors, then realize that macOS Catalina, Big Sur, and Monterey only support 64-bit applications, printer, and scanner drivers. Use the free Go64 application to look at your 32-bit applications before you leap.
Make certain that you have a last Time Machine backup before performing any upgrade, and do not let the new operating system perform Time Machine backups to that drive.