New iPad Air , how to connect to Apple TV? Can’t swipe up to get to control center.

From this support document, Use and customize Control Center on your iPhone, iPad, and iPod touch - Apple Support

Open Control Center

Swipe up from the bottom edge of any screen. On iPhone X or later or iPad with iOS 12 or later, swipe down from the upper-right corner of the screen.

I believe on newer devices Control Center is accessed by swiping downward from the upper right corner of the screen.

I would say the latest iPad Air has iOS 12 or later, which complies with the information I provided. I'm glad you were able to get it to work for you.