This is already possible via a browser extension but the extension only technically moves the new tab after it has been moved and takes over the functionality of clicking hyperlinks (which I would expect to end up at the end of the row. Firefox has an option for enabling this via browser.tabs.insertAfterCurrent .
But the ideal situation would be a new hotkey. When using use only the keyboard this functionality would be extremely helpful. Combined with a shortcut editing someone would be able to customize they prefer out of the default shortcut (although the new tab functionality from hyperlinks should really be a setting).