Slander about to cover Republican one's beaten (4)
I believe the answer is:
drum
'one's beaten' is the definition.
(you beat a drum to play it)
'slander about to cover republican' is the wordplay.
'slander' becomes 'mud' (as in to drag someone's name through the mud).
'about' says the letters should be written in reverse.
'to cover' indicates putting letters inside.
'republican' becomes 'r' (abbreviation).
'mud' in reverse letter order is 'dum'.
'dum' enclosing 'r' is 'DRUM'.
(Other definitions for drum that I've seen before include "Thing to be beaten - but not as a container!" , "Cylindrical metal container" , "See 18" , "Percussion instrument" , "Tap" .)