Headrest has base supporting raised edge (6)
I believe the answer is:
pillow
'headrest' is the definition.
(I've seen this in another clue)
'base supporting raised edge' is the wordplay.
'base' becomes 'low' (synonyms).
'supporting' says to put letters next to each other (in a down clue, some letters go below others).
'raised' says the letters should be written backwards (going up in a down clue).
'edge' becomes 'lip' (lip is a kind of edge).
'lip' back-to-front is 'pil'.
'low' after 'pil' is 'PILLOW'.
'has' acts as a link.
(Other definitions for pillow that I've seen before include "Sleeper's cushion" , "Cushion for head" , "Sleeper's support" , "place to lay his head" , "Soft place for the head" .)