Given up before, this smoker (4)
I believe the answer is:
etna
'smoker' is the definition.
(volcano Mount Etna, something which 'smokes')
'given up before' is the wordplay.
'given up' shows that the letters should be reversed in order (in a down clue, letters go up).
'before' becomes 'ante' (prefix meaning 'before').
'ante' written backwards gives 'ETNA'.
'this' acts as a link.
(Other definitions for etna that I've seen before include "feature spewing lava" , "Volcano; reverse of stake" , "high peak" , "It could erupt" , "Volcano in Italy" .)