How do I update Safari for my iPad?

Safari is an integral element of iOS/iPadOS - and cannot be updated independently of the OS. If your iPad has been updated to the most recent version supported by your iPad (the model and installed version of iOS have not been declared), then Safari is as up-to-date as is possible.

The tags appended to your post suggest that you have an iPad4 with iOS10 installed. This may be the root of your problem.

Update support for iPad4 ended September 2017. The final iOS releases for this model were iOS 10.3.3 (WiFi Only models) and iOS 10.3.4 (WiFi & Cellular). iPad4 cannot be updated to any later major version of iOS as it lacks the minimum hardware requirements needed to run more recent versions. The 32-bit platform upon which the iPad4 is built is obsolete.

When browsing websites, your “user agent” (the web Browser) needs to be compatible with the website - most pages on modern websites being “rendered” for display on your device screen. If the web browser is no longer adequate to work with the web site, errors are likely to be reported - or the website simply won’t work as expected.

The Safari browser is an integral element of the Operating System - and can only be updated along with the OS. A peculiarly of iOS/iPadOS is that all third-party web browsers must use core elements of the OS - specifically an element known as WebKit. Even if you are still able to find a compatible third-party browser Apps for your obsolete iPad, it is perhaps unlikely to resolve your immediate problem with browser issues.

Many App Developers have dropped support for older devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store. Withdrawal of Apps supporting older models of iPad is making their utility and usefulness significantly more limited.

If Apps (or your browser) that you need to use now have higher minimum iOS-version requirements, or websites that you visit require an up-to-date (i.e., supported) Operating System or browser, your only option is to replace your iPad with newer model.

Of current models, even the entry-level iPad8 supports current iPadOS 14 - and has hardware specifications and capabilities that vastly outperform your old iPad4.

I hope this information is helpful - if only in clearly stating the limitations of your iPad4 and your available options.

Safari updates automatically when you update iOS.

Update your iPhone, iPad, or iPod touch - Apple Support

You probably have an iPad fourth generation released in 2012, and that model lacks the hardware and particularly the memory necessary for newer iPadOS releases. What to do, to get newer iOPadOS, and newer Safari? There are no hardware upgrades for any iPad. The only option when newer iPadOS is required is a newer or new iPad. Any recent iPad will bE vastly more capable than the iPad fourth generation, too.