In Apple System Preferences I do not have the option of Software Update. I have the mac OS High Sierra Version 10.13.6. In About This MAC, Software Update, I get No App Updates Available. How can I get the latest version?

Back up your data, check your applications for compatibility, and depending on which MacBook Pro model you have, click on Mojave, Catalina, or Big Sur. It needs to be at least a 2012 one to run a newer OS.

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How to upGrade from High Sierra

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the apple Store when one can commence the download.

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina & Big Sur supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation

It didn't appear in Sys Prefs until 10.14 Mojave. :)

macOS Mojave 10.14.6 - Technical Specifications

General Requirements

OS X 10.8 or later

2GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible Internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Mojave:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with recommended Metal-capable graphics cards)

Don't use FireFox for these links…

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

MacOS Catalina 10.15.7 - Technical Specifications

General Requirements

OS X 10.9 or later

4GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013 or newer)

https://support.apple.com/en-us/HT210190

Don't use FireFox for these links…

https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12

How to upgrade to macOS Catalina – Apple Support

And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...

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

macOS Big Sur - Technical Specifications

General Requirements

OS X 10.9 or later

4GB of memory

35.5GB available storage on macOS Sierra or later*

Some features require an Apple ID; terms apply.

Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Big Sur:

MacBook (2015 or later)

MacBook Air (2013 or later)

MacBook Pro (Late 2013 or later)

Mac mini (2014 or later)

iMac (2014 or later)

iMac Pro (2017 or later)

Mac Pro (2013 or later)

Learn about compatibility and how to identify your specific Mac model

Don't use FireFox or WaterFox for this link. it'll mess it up...

https://apps.apple.com/us/app/macos-big-sur/id1526878132?ls=1&mt=12

And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...

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

I have the option to update but it goes through the process of downloading and once it gets to the end it never completes and install. It just stays saying ex. 21.4 of 21.4 so you know it got to the end but it just don't complete, and this was with all 3 different OS updates since Mojave.4

I have a 64 bit but I still cannot upgrade my software past Mojave. What can be the issue?

Is your MacBook Pro Mid 2012 or 2013?

The Question- what is the AGE of This Computer may even answer you own question.

We are not there it see this information

No 2015

MacBook Air (13-inch, Early 2015)

Try it in Safe Mode...

Safe Boot, (holding Shift key down at startup), does the problem occur in Safe Mode? Could take 10 minutes.

I'll try

Thank you so much. After over a year I finally upgraded my OS, and am now up to date! :)

Great to hear my friend, do take care! :)