we have an IMAC 21.5 inch - Mid 2014 - model which shows all features and software as up to date. We are currently running Safari 13.1 but have been asked to upgrade for security reasons to Safari 14.1. Is there any way to do this on our computer?

Safari gets updated along with the macOS. You may want to consider updating the macOS for this one.

But before you update, it's a good idea to create a backup first to avoid data loss.

Update to the latest version of Safari - Apple Support

You can also try updating it via the App Store

How to manually update apps on your Apple device - Apple Support

And it looks like your iMac can still be upgraded to macOS Catalina

How to get old versions of macOS - Apple Support

Hope this helps!

That is easier to answer if you tell us the macOS version your computer is currently running.

I'm guessing—and that is never good— that you are running macOS 10.13 "High Sierra." Although your computer will support up to macOS 11 "Big Sur," you may not want to got that far.

Your Mid 2014 is the crippled "educational/institutional" model with a slow 1.4Ghz 2-core laptop processor. Regular iMacs had a faster 4-core desktop-class processor. You may find the slow processor is really challenged by Catalina or Big Sur.

iMac (21.5-inch, Mid 2014) - Technical Specifications

The last macOS to support older 32-bit software was Mojave 10.14. If you have old versions of expensive software like Adobe Creative Cloud/Suite, or MS Office older than Office 2016. they will not run if you go past 10.14 Mojave See:

32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

This free tool can find and report on any 32-bit apps you have:

https://www.stclairsoft.com/Go64/