A bit of backbone is found in Washington (4)
I believe the answer is:
disc
'a bit of backbone' is the definition.
(part of the spine)
'is found in washington' is the wordplay.
'found in' indicates putting letters inside.
'washington' becomes 'dc' (Washington DC).
'is' put within 'dc' is 'DISC'.
(Other definitions for disc that I've seen before include "Part of flower" , "counter" , "Layer of cartilage between spinal vertebrae" , "Thin circular plate, as in CD" , "Back part" .)