I'm trying to update Acrobat Express on my MacBook...but it says I need to have macOS Ventura 13.0. My s

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 where the download can commence.

Does this computer appear as Listed and qualifying for an upGrade to a newer version of macOS ? 

If Yes, suggest having at least 50 GB of Empty Space on the drive.

It will allow the Full Version ( about 12.xx GB ) to download, expand and then commence to install.

If there is Third Party Security Software installed - remove it.

It will interfere with both the download and installation process.

The below links will help identify which version of macOS  this computer may Qualify to run.

Computer Qualifying for macOS 13 Ventura 

How to upgrade to macOS Ventura - Apple Support (CA)

Computer Qualify for the Monterey upgrade

macOS Big Sur 11 hardware requirements

Make Time Machine Backup  is very useful 

JennDoug74 wrote:

Now I'm being prompted saying I need to update my macOS to Ventura 13.0, it is currently on my system as macOS Catalina 10.15.7 it will not update any further apparently. Why is that? What do I need to do?

Where did you see you have to have Ventura for Adobe Express? According to this page: Adobe Express system requirements, AE requires macOS 10.13 High Sierra or later.

Why would I update to an old version of something with how to get old versions of macOS?

There are several versions of macOS there that are newer than what you have.

Are you saying I just go to the App Store and look for macOS Ventura and upload it?!

Yes, except you need to download the installer. You can’t upload anything to the App Store.

It is entirely possible your Mac is not capable of running Ventura. You can find older versions that may run on your Mac at the link I provided. The linked article also has a link to Ventura.

Unless I have misread the Adobe requirements and overview of AE, this is a web-based, or phone based application and there is no Windows or macOS version of it unless that is hidden behind the sign-in door, as I see no downloads for either operating system.

So as you have posted above, it appears to be finicky with the browser used to access it.

Moving from 10.15 to a following OS is an upgrade, not an update. you have to check in the App Store or here:

How to get old versions of macOS - Apple Support

FWIW, I booted a 2012 iMac I still have running Catalina 10.15.7. Adobe Express will not open in Safari but it does open in Google Chrome.

No, you read them correctly. Hence my screen shot of Chrome running Adobe Express beta. 😎

VikingOSX wrote:

So as you have posted above, it appears to be finicky with the browser used to access it.

It runs in Safari in Monterey. I haven't checked Big Sur.