Blunder finally across border (4)
I believe the answer is:
slip
'blunder' is the definition.
(slip is a kind of blunder)
'finally across border' is the wordplay.
'finally' indicates one should take the final letters.
'border' becomes 'lip' (I've seen this in other clues).
The final letter of 'across' is 's'.
's'+'lip'='SLIP'
(Other definitions for slip that I've seen before include "Lose footing or make mistake" , "Man in field" , "Slight error" , "shift" , "Mistake; garment" .)