The most common and most likely answer to this crossword clue is the 12 plus 3 letter word INDEPENDENCE DAY
I've seen this crossword clue in The Times
I
N
D
E
P
E
N
D
E
N
C
E
D
A
Y
More clues leading to the result INDEPENDENCE DAY
Buddy explains!
The straight part
We know that "anniversary/" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case anniversary/ = independence day.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.