Caught at rack initially taking favourite dress down (6)
I believe the answer is:
carpet
'dress down' is the definition.
(I've seen this before)
'caught at rack initially taking favourite' is the wordplay.
'initially' indicates taking the first letters.
'taking' is a charade indicator (letters next to each other).
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
The first letters of 'caught at rack' is 'car'.
'car'+'pet'='CARPET'
(Other definitions for carpet that I've seen before include "blanket" , "roll of fabric?" , "Tick off" , "Tear a strip off" , "Runner perhaps" .)