Automatic, having rug (3)
I believe the answer is:
mat
'rug' is the definition.
(both are floor coverings)
'automatic having' is the wordplay.
'having' says the answer is hidden in the clue.
'MAT' is hidden in the letters of 'automatic'.
(Other definitions for mat that I've seen before include "Rug; without a shine" , "coaster" , "Small carpet" , "Piece of material for wiping feet on" , "Not glossy" .)