Worn-down pencil (3)
I believe the answer is:
nub
'worn-down pencil' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for nub that I've seen before include "Core, pith or gist" , "'Gist, central idea (3)'" , "Crux, central point" , "Centre point or core of a matter" , "Central point of bun" .)