can I reinstall only Mac OS high Sierra from time machine after the Mac HD has been completely erased/

If I understand what you’re asking, you’d like to completely erase your Mac and upgrade the operating system to Mac OS High Sierra without actually going thru the upgrade process from your original MacOS. You wamt

to take a blank state hard drive and install Mac OS Sierra as a new machine with the hardware and memory that were designed for an earlier version of MacOS. Why don’t you just buy a new Mac with hardware and memory that have been configured to the specifications that the engineers for MacOS Sierra specify as being optimal fo meet the requirements to run Mac OS Sierra? Your playing a fools game to save a buck.

This article from Apple and Specific to macOS 10.13 High Sierra should provide the needed information for what you are asking

Link below

Recover all your files on Mac - Apple Support (CA)