The record is held by the District of Columbia (4)
I believe the answer is:
disc
'the record' is the definition.
('disc' can be a synonym of 'record')
'is held by the district of columbia' is the wordplay.
'held by' indicates putting letters inside.
'the district of columbia' becomes 'dc' ('DC' can be a synonym of 'district of columbia').
'is' going within 'dc' is 'DISC'.
(Other definitions for disc that I've seen before include "45, eg?" , "Old record" , "something moving in the spine" , "Sound recording" , "Protein-constituent acid" .)