Drag carrying exercise mat (6)
I believe the answer is:
carpet
'mat' is the definition.
(thesaurus)
'drag carrying exercise' is the wordplay.
'drag' becomes 'cart' (synonyms).
'carrying' means one lot of letters goes inside another.
'exercise' becomes 'pe' (Physical Education).
'cart' going around 'pe' is 'CARPET'.
(Other definitions for carpet that I've seen before include "What may deaden sound in room" , "Reprimand, reprove" , "blanket" , "Tick off" , "that probably won't be seen on the factory floor?" .)