Can my 2017 MacBook Air run macOS 13 or above?

It's not going to happen.

Monterey is the highest supported version of macOS for that machine – and whatever Apple's reasons for drawing the cutoff point for Ventura where they did, they're not going to go back and revisit that decision now.

If Apple sticks to the same release schedule that they have for the last ten years, Sequoia's successor will come out this September, October, or November. At that time, Ventura will drop off the list of "the most recent three" and you will find vendors like Adobe and Microsoft starting to drop support for it.

Then you'd need to be able to run Sonoma on that machine to keep up …

"Can my 2017 MacBook Air run macOS 13 or above?: Is there any chances to rollout Mac OS 13 and above for the MacBook Air 2017 devices."

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Updating a 2017 MBA to macOS 13:

No. See here: macOS Ventura is Compatible with these Computers - Apple Support

No. Its CPU isn't powerful enough.

(260035)

There are applications that you can get that may help you to prolong the useful life of that 2017 MacBook Air.

Monterey is still good enough to run current versions of

• The Firefox web browser
• The Brave, Opera, Microsoft Edge, and Google Chrome browsers
• The LibreOffice office suite
• The GNU Image Manipulation Program (GIMP)
• The commercial Affinity V2 applications (Photo, Designer, Publisher)

plus the backup utilities CCC v6 (not current, but still supported) and SuperDuper! (For that matter, some of these applications will run on Catalina.)