Simply copy the URL of the web page to your clipboard. Then delete the tab, create a new tab (by clicking on the New Tab button, pasting the clipboard into the address bar, then pressing Enter), and click Pin Tab on the new tab. Your pinned tab will be without any history!

Note that Firefox 67 comes with a "Pin Tab" item in the tree-dot page actions menu. If you pin a tab regularly then right-click this item => Add to Address Bar. You can duplicate a tab without history via Alt+Enter in the address bar and then click the "..." button to pin the tab.

Not sure I understood these instructions. Also, when I click the three dots in FF 67.0.1, I see no "Pin Tab" item, not even under the "More..." item. Nor do I see an "Add to Address Bar" item in the Right Mouse Button Menu for a pinned tab.

This is about the three dot page action button next to the star on the location bar and not about the three bar menu button.

Screenshot.

Thank you for your kind clarification. In my opinion the term "tree-dot page actions menu" is jargon. An ordinary user cannot tell which of the three-dot menus is which, except by location on the page. That is a problem in choosing to name a menu item ambiguously using three dots (another being that it may not be accessible at all to blind and visually impaired people--I haven't checked this here).

Readers are free to choose the answer that seems clearest to them, even if your answer is technically better.