Many editors do not handle some HTML elements well and will prevent you from inserting icons or if you're in the WISIWYG mode will appear as a blank space but switching to HTML view you'll see the FA code there.
We recommend using the CodeMirror editor which can be enabled in the Joomla Global Configuration of your site.
TinyMCE tends to block the needed "" tags that FontAwesome uses.
The JCE Editor will display icons for you in the editor with some adjustments to the JCE Global Settings.
If you are using JCE go to Components > JCE Editor > Global Configuration
In the Format & Display section change Editor Styles to "Custom CSS" and add the following to the Custom CSS Files section:
plugins/editors-xtd/ns_fontawesome_pro_btn/assets/css/font-awesome.css
Then set Compress CSS to "No" (For some reason JCE can't handle compressing the FA CSS files).

Save your setting and you now should be able to see the icons in the editor. Note the icons won't be styled in the editor view because the styling is applied on the front end via CSS but you'll at least be able to see there's an icon there.
Tip: If you find yourself switching between editors ofter you should grab the Editor Switcher plugin by Anything-Digital. It adds a selector to the bottom left corner of your admin side which makes it super easy to switch between editors without having to bounce back to the Global Config every time.