Second successful person, not the first, is a baddie (6)
I believe the answer is:
sinner
'baddie' is the definition.
(a bad person)
'second successful person not the first' is the wordplay.
'second' becomes 's' (common abbreviation).
'successful person' becomes 'winner' (a winner has had success).
'not the first' means to remove the first letter.
'winner' with its initial letter taken off is 'inner'.
's'+'inner'='SINNER'
'is a' acts as a link.
(Other definitions for sinner that I've seen before include "One in breach of moral law" , "Miscreant" , "One morally corrupt" , "Wrong-doer" , "Immoral transgressor" .)