Can macOS High Sierra 10.13.6 be updated?

If you're trying to install a security or other update, yes, if there's a version of it for High Sierra.

If you're trying to upgrade the computer's OS, only if your Mac is a 2012 or newer model, or a 2010 desktop Mac Pro upgraded with a Metal-capable graphics card.

(201039)

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. Make sure to use Only Safari to commence the download as Other may not work

Make a Time Machine Backup Before attempting. Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina and Big Sur Only support 64 bit and there is no workaround.

Are there any AntiVirus, Disk Cleaner, Optimizers, Defrag, VPNs 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.