will my photoshop elements 2019 work on a Mac running iOS 15.2

My bad... I meant OS. 

 a Mac running iOS 15.2

By @bob_4492

We know what you mean, but FYI, here is a technical point:

Mac iOS is a mobile operating system, and Premier Pro doesn't run on mobiles.

You mean Mac OS 15.2.

Bob, I always go straight to the horse's mouth for the answer:

System requirements | Older Versions

Excerpt from 2019 section:

• 64-bit multicore Intel processor
• macOS X v10.14, v10.13, or v10.12
• 4GB of RAM (8GB recommended)
• 6.5GB of available hard-disk space (additional free space required during installation and additional 2.5GB to download all optional content)
• 1280x800 display resolution (at 100% scale factor)
• DVD-ROM drive (for installation from DVD)
• Internet connection required for product activation and content download*
• Supported browsers: Safari 7.x or later, Mozilla Firefox 4 or later, or the latest version of Google Chrome
  
  
• Note:

  You cannot install Photoshop Elements 2019 on a volume that uses a case-sensitive file system or on removable flash storage devices.