The most common and most likely answer to this crossword clue is the 5 plus 2 plus 8 letter word THIRD OF NOVEMBER
I've seen this crossword clue in The Guardian
T
H
I
R
D
O
F
N
O
V
E
M
B
E
R
Buddy explains!
The straight part
We know that "day" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case day = third of november.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.