Opens Safari's current tab in a new private window and closes the tab. If a private window already exists, then opens the current tab in that window.

gistfile1.applescript

tell application "Safari"
	activate
	set theURL to the URL of the current tab of the front window
	close current tab of front window
end tell

tell application "Safari"
	activate
	set theWindow to false
	repeat with w in (every window whose visible is true)
		set theMode to do JavaScript "try {localStorage.setItem('foo', 'bar');} catch(e) {modevar=4}" in current tab of w
		if theMode = 4 then
			tell application "Safari"
				tell w
					set theTab to make new tab
					set the URL of theTab to theURL
					set current tab to theTab
					set index to 1
				end tell
			end tell
			set theWindow to true
			exit repeat
		end if
	end repeat
	
	if not theWindow then
		tell application "System Events"
			tell process "Safari"
				tell menu bar 1
					click menu bar item "File"
					tell menu "File"
						click menu item "New Private Window"
						tell application "Safari"
							set URL of document 1 to theURL
							set index of document 1 to 1
						end tell
					end tell
				end tell
			end tell
		end tell
	end if
end tell