Rope holds up dog biting artist (6)
I believe the answer is:
lariat
'rope' is the definition.
(lariat is a kind of rope)
'holds up dog biting artist' is the wordplay.
'holds up' says the letters should be written backwards (I've seen 'held up' mean this).
'dog' becomes 'tail' (synonyms).
'biting' indicates putting letters inside (I've seen this in other clues).
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'tail' going around 'ra' is 'tairal'.
'tairal' in reverse letter order is 'LARIAT'.
(Other definitions for lariat that I've seen before include "Mortar-spreading tool" , "Rope for the cowboy" , "Cowboy's rope, lasso" , "A trail (anag) - rope" , "Rope used as a lasso" .)