This is an Eberhard Faber Mongol cap and extender (with an A.W. Faber No. 3 pencil).
But it’s not quite the extender in this advertisement:
Most of the paint has been worn off but the Mongol band is still distinct, and the sliding ring works perfectly; not bad for being around 100 years old (same goes for the pencil). I think I’d like to paint this black again and restore it but I’m not sure what kind of paint to use.