Deaden the sound of animal going about very loudly (6)
I believe the answer is:
muffle
'deaden the sound of' is the definition.
(I've seen this in another clue)
'animal going about very loudly' is the wordplay.
'animal' becomes 'mule' (offspring of a donkey and a horse).
'going about' means one lot of letters goes inside another.
'very loudly' becomes 'ff' (short for fortissimo, 'very loud' in music).
'mule' going around 'ff' is 'MUFFLE'.
(Other definitions for muffle that I've seen before include "Cover (to block sound)" , "damp" , "Suppress sound as with silencer" , "Keep warm" , "(Device to) reduce sound" .)