Possible Clues:

• Toothless thank you note written by former PM
• Garden rubbish -- right tip belonging to some sloth?
• Mammal of an order which includes sloths, anteaters and armadillos
• Country's leader going to display sloth, say
• Sloth, say, in garden with place for art
• Online chat about ear, nose and throat, but teeth? None
• Toothless old prime minister installed as head of state
• Sloth maybe in UK tourist hotspots
• Sloth, say, attendee suffered
• Maybe anteater in garden, say, hiding head