The most common and most likely answer to this crossword clue is the 8 letter word ONE-TIME
I've seen this crossword clue in The Guardian
O
N
E
-
T
I
M
E
More clues leading to the result ONE-TIME
- Former ace, a man with energy
- Former England 5 comes in promptly
- 7 Previously pitiable mite noticed turning up exhibits
- Previous jail sentence under twelve months
- Former opener for Essex enters punctually
- Late drink, when pub stops serving
- Former love, overall, beginning to irritate me
- Former old means of communication with two setters
- Former writer’s pursuing goal in Old English
- Former marriage following love not once
Buddy explains!

The straight part
We know that "Late" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case late = one-time.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ONE-TIME mean?
ONE-TIME noun- The police.
- To shoot (the ball or puck) directly from a teammate's pass.
- Of or pertaining to a specific time in the past.
- Occurring on only one occasion.