Can I upgrade my mac air book from mac 0S High Sierra version 10.13.16 to current mac air OS

What model year is it?

The model year of a MacBook Air is available at Apple menu > About This Mac.

A late 2010 through mid 2011 MacBook Air can be upgraded to High Sierra 10.13.6 but no later version. See: How to download macOS - Apple Support

A mid 2012 MacBook Air can be upgraded to Catalina 10.15.7 but no later. See: How to download macOS - Apple Support

A mid 2013 and early 2014 MacBook Air can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to download macOS - Apple Support

An early 2015 and a 2017 MacBook Air can be upgraded to the latest version of Monterey macOS 12. See: How to download macOS - Apple Support

A 2018 or later MacBook Air can be upgraded to the current version of Ventura macOS 13. See: How to upgrade to macOS Ventura - Apple Support

Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

If you can't or don't want to upgrade your macOS, for security reasons you should consider using a 3rd party internet browser that supports their current version with your older macOS. Two examples are Chrome https://www.google.com/chrome/ or Firefox.

Upgrading a macOS depends upon the model Mac, specifications, and year. To get more information about your computer, choose:  (Apple menu) > 'About This Mac' in the upper left corner of any window, then "More Info..." or "System Report". There's more about this in "About System Information [Profiler] on your Mac" - System Information User Guide for Mac - Apple Support

Use the computer information, including the model year, and the links below to determine what is possible with your computer.

Click on this link to read how to get different versions of macOS --> How to download macOS - Apple Support

- The article also has links to system requirements for each OS version which you should check against your exact computer model. For any model produced in the last 5 years or so you should use the system requirements links for each OS version instead. This web site also has a reliable presentation of model and OS version compatibility: https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

- It helps to have more RAM (memory) than what is noted as "minimum" for any particular system or your computer may run slowly.

- You may find you must use Safari to get links for High Sierra and later using the Mac App Store application to open to a functioning page.

- Sierra, El Capitan, and Yosemite download as a .pkg. Click on this to have a converted version placed in your Applications folder as an "Install OS..." application. Run the installer and follow the directions.

- Upgrades may take some time (up to an hour or more) to install, with restarts and blank screens.

Before upgrading, back up at least your data in case something goes wrong. See this support document: How to back up your Mac - How to back up your Mac - Official Apple Support

Check if your old apps will still work with with the OS you want to install - https://roaringapps.com/apps This is particularly critical if you are upgrading to Catalina or newer, as older 32 bit apps will no longer work. To check for those, try this 32 bit application scanner application --> https://www.stclairsoft.com/Go64/

If an error occurred while updating or installing macOS --> If an error occurred while updating or installing macOS - Apple Support

I don't think so. MacTracker seems to indicate that there are no MacBook Airs capable of running the whole range of operating systems from High Sierra to Ventura. The oldest one that can run Ventura shipped with Mojave.

You may be able to upgrade to a newer version of macOS – possibly up to macOS 12 Monterey, if your machine is new enough. It's impossible to say how far you can upgrade without knowing what specific MacBook Air you have. Please select About This Mac in the Apple () menu and tell us the full model name shown there.