How do I update my MacBook Air 13 to the latest OS?

Did you already check the links in this article?

How to download and install macOS - Apple Support

But, if the hardware of your MacBook Air does not support any further maOS upgrades, you can not install them manually.

darlingdeb wrote:

I have updated what is available to me but I need a more current OS for a download (bold mine)

If you've reached the maximum OS for your computer, you cannot upgrade any further. You'll have to find a substitute for the program or buy a newer computer.