Drag gripping exercise mat (6)
I believe the answer is:
carpet
'mat' is the definition.
(thesaurus)
'drag gripping exercise' is the wordplay.
'drag' becomes 'cart' (synonyms).
'gripping' means one lot of letters goes inside another (inserted letters are gripped).
'exercise' becomes 'pe' (Physical Education).
'cart' going around 'pe' is 'CARPET'.
(Other definitions for carpet that I've seen before include "Heavy fabric for floors" , "blanket" , "Tell off" , "roll of fabric?" , "Woven fabric for the floor" .)