The most common and most likely answer to this crossword clue is the 9 letter word FIREWORKS
F
I
R
E
W
O
R
K
S
Buddy explains!

The straight part
We know that "New Year display" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case new year display = fireworks.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 FIREWORKS mean?
FIREWORKS noun- A device using gunpowder and other chemicals which, when lit, emits a combination of coloured flames, sparks, whistles or bangs, and sometimes made to rocket high into the sky before exploding, used for entertainment or celebration.
- An event or a display where fireworks are set off.
- A boisterous or violent event or situation.