Second best and late, break off abruptly (4,4)
I believe the answer is:
stop dead
'break off abruptly' is the definition.
(to stop dead is to stop suddenly)
'second best and late' is the wordplay.
'second' becomes 's' (common abbreviation).
'best' becomes 'top' (top can mean the very best).
'and' is a charade indicator (letters next to each other).
'late' becomes 'dead' (similar in meaning).
's'+'top'+'dead'='STOP DEAD'
(Other definitions for stop dead that I've seen before include "Pull up abruptly" , "Become immobilised" .)