Abandon hope as a spider runs out (7)
I believe the answer is:
despair
'abandon hope' is the definition.
('despair' can be a synonym of 'abandon hope')
'a spider runs out' is the wordplay.
'runs' indicates an anagram.
'out' means one lot of letters goes inside another.
'spider' with letters rearranged gives 'despir'.
'a' placed inside 'despir' is 'DESPAIR'.
'as' is the link.
(Other definitions for despair that I've seen before include "Total loss of hope" , "A spider (anag.)" , "Lose heart" , "Opposite of 10" , "sort of counsel?" .)