To exist is the reverse of wicked (4)
I believe the answer is:
live
'to exist' is the definition.
(synonyms)
'the reverse of wicked' is the wordplay.
'the reverse of' shows that the letters should be reversed in order.
'wicked' becomes 'evil' (synonyms).
'evil' in reverse letter order is 'LIVE'.
'is' is the link.
(Other definitions for live that I've seen before include "Present in person, not recorded" , "Dwell" , "As it happens - exist" , "Electrically charged" , "A . . . . wire is a highly energetic person" .)