The most common and most likely answer to this crossword clue is the 3 plus 6 plus 3 letter word NEW YEAR’S EVE
I've seen this crossword clue in The Guardian
N
E
W
Y
E
A
R
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€
™
S
E
V
E
More clues leading to the result NEW YEAR’S EVE
Buddy explains!
The straight part
We know that "Time to chuck out the old" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case time to chuck out the old = new year’s eve.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.