How do I update Safari on my Mac?

Safari is updated when MacOS is updated, it cannot be updated outside of an OS update. I note that you have a MacBook Pro running High Sierra (10.13). This is now 5 versions old. If that's the latest version your MBP can run, then that would intimate that you computer is at least 10 years old (it's a 13" MBP running 10.13. That was the last version mid and late 2011 models could run). Further evidence of this is if you are no longer receiving update notifications.

If that's the case, then you really need to think about replacing your computer.