Succeeding in goal without evidence of mistake (4)
I believe the answer is:
next
'succeeding' is the definition.
(next in a sequence)
'goal without evidence of mistake' is the wordplay.
'goal' becomes 'net' (net is a kind of goal).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'evidence of mistake' becomes 'X' (X can indicate an error).
'net' placed around 'x' is 'NEXT'.
'in' is the link.
(Other definitions for next that I've seen before include "Coming immediately" , "Coming nearest in order - come, please!" , "Neighbour lives in the house . . . . door" , "The second cherry stone on the plate" , "Coming nearest in time or sequence" .)