Update to Big Sur

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Would suggest upGrading to High Sierra macOS 10.13 first. This version of OS X is very very old and out dated. This step to HS may better position the computer with a possible Drive Conversion to APFS and also may bring EFI BOOT ROM updates to the computer allowing it to use and understand the new APFS format.

Safari will open a redirect and open the Apple Store where the download can commence

Tips Big Sir Upgrade Released Nov 2020

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal  operation of the OS and may even Corrupt the OS requiring a Reinstallation

Back up your data, check your applications for compatibility, and depending on which MacBook Air model you have, click on El Capitan, High Sierra, Mojave, Catalina, or Big Sur.

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