Fail to work, having succeeded in objection (2,4)
I believe the answer is:
go bust
'fail' is the definition.
(as in a business going bust)
'work having succeeded in objection' is the wordplay.
'work' becomes 'go' (synonyms).
'having' is a charade indicator (letters next to each other).
'succeeded' becomes 's' (genealogical abbreviation).
'in' means one lot of letters goes inside another.
'objection' becomes 'but' (as in 'no ifs, no buts').
's' put inside 'but' is 'bust'.
'go'+'bust'='GO BUST'
'to' is the link.
(Other definitions for go bust that I've seen before include "Not get out of the red" , "so firm might collapse" , "Become bankrupt" .)