What to propose should work. You will need to boot to internet macOS Recovery to install macOS. See the Apple website: How to reinstall macOS. When booted to macOS Recovery, you will probably have to use the Disk Utility to initialize, before installing macOS. If this does not install High Sierra, then you will need to download and install High Sierra from the Apps Store. This is the easiest way to get the latest firmware Updates.
When changing drives, you may need to hold down the option key at startup to invoke the Startup Manager. To make a desired operation system the default, hold down the control before selecting the arrow.