How to update to newer OS?

Macs don't run iOS. They run macOS.

Which versions of macOS you can run depends on your hardware model. If you go into the Apple () menu, and select About This Mac, what does it say for the model name (including year and time of year)?

For a MacBook Air,

• If the name includes "Mid 2013" or "Early 2014", macOS 11 (Big Sur) is the end of the line.
• If the name includes "Early 2015" or "2017", macOS 12 (Monterey) is the end of the line.
• If the name includes "2018", "2019", "2020", "M1", or "M2", the Air can run macOS 13 (Ventura).

You may need to spend some money.

Explore the Apple Trade-In  Process where the Value of the exiting device could be used against the cost of a new Apple Computer, iPhone or iPad 

Notation - Some devices and depending on the computers age may have little to no value at Trade In time.

But at least the device will not arrive to the Land Fill Site and be recycled in a responsible way by Apple

Or Shop Refurbished Apple computers at an Apple Reduced Cost

Have used both previously and have been satisfied each time.