How to update Safari on my MacBook Pro

Chase Bank is the only such institution doing that. It is their problem to fix. They need to stop using the outdated and privacy-intrusive "user agent" query. Unfortunately, that leaves you out in the cold until they realize the error of their ways and correct it.

The workaround for end users who are unable to update their Macs to a newer macOS version is to use a different browser.

Consider Brave:

https://brave.com/

Firefox is a distant second choice:

https://www.mozilla.org/en-US/firefox/new/

The bottom line is that there is nothing wrong with your Mac's version of Safari, but that bank is using an outdated and ill-conceived method of determining browser requirements. If you are so motivated direct their attention to the WWW publication User-Agent Client Hints (courtesy VikingOSX).

In-depth background discussion here: chase wants me to update safari to 16, should I do that? - Apple Community

Safari is usually updated with macOS, so a macOS update or upgrade would be typical.

Safari 16 is available for macOS 11 Big Sur and later, so that means a Mac Pro 2013 or Mac Pro 2019 model (based in your reply), or means a MacBook Pro (based in where this was posted).

Mac Pro 2013 can get to macOS 12 Monterey, so fairly recent and can run Safari 16.

Mac Pro 2019 can get to the current macOS 14 Sonoma, so that too can run Safari 16.

Older Mac Pro models can’t get to macOS with Safari 15.

Which macOS a MacBook Pro can get to varies by MacBook Pro model year.

if you have a MacBook Pro, which year? (See the Apple menu > About This Mac for that info.)

And which macOS is this Mac currently running? (Version info is available in About This Mac, too.)

Here is how to get older versions of macOS: How to download and install macOS - Apple Support

If your MacBook Pro is older and cannot be upgraded, then a more recent browser with support for older versions—such as Mozilla Firefox—might work.