Continually drag donkey behind tethers (5-5)
I believe the answer is:
chain-smoke
'continually drag' is the definition.
(continually smoke cigarettes)
'donkey behind tethers' is the wordplay.
'donkey' becomes 'moke' (moke can informally mean a donkey).
'behind' means one lot of letters go next to another.
'tethers' becomes 'chains'.
'moke' put after 'chains' is 'CHAIN-SMOKE'.
(Other definitions for chain-smoke that I've seen before include "Light one fag after another" , "Get through cigarettes one after another" , "Get through fags one after the other" , "Puff non-stop" , "Keep dragging" .)