The age of your MacBook Air hardware determines if you can upgrade to a newer operating system or not.
Visit Apple menu () : About This Mac and observe the product description line. Look at what is in parenthesis and then determine from the following if your Air supports an upgrade to:
macOS Catalina is compatible with these computers - Apple Support
macOS Big Sur is compatible with these computers - Apple Support
macOS Monterey is compatible with these computers - Apple Support
If you can satisfy the hardware requirements for one of these operating systems, you can obtain the full installer using the Safari browser from:
How to download and install macOS - Apple Support
Do not attempt an operating system upgrade without first backing up your Mac with Time Machine.
Note. None of the listed operating systems above support any 32-bit applications, printer/scanner drivers, or other 32-bit dependencies. Use the free Go64 application to get a list of these, and determine its impact on your upgrade plans. Visit third-party vendors of your installed applications and note if their currently available applications support one of the above operating systems.