Relish slander involving big name (7)
I believe the answer is:
mustard
'relish' is the definition.
(I have seen 'Hot relish ' mean 'mustard' so perhaps 'relish' could also mean 'mustard')
'slander involving big name' is the wordplay.
'slander' becomes 'mud' (as in to drag someone's name through the mud).
'involving' means one lot of letters goes inside another.
'big name' becomes 'star' (I've seen this in another clue).
'mud' going around 'star' is 'MUSTARD'.
(Other definitions for mustard that I've seen before include "Powdered seeds used to make condiment" , "Yellow paste as condiment - very keen" , "The colour" , "Hot condiment" , "It gives a bit of a kick" .)