The most common and most likely answer to this crossword clue is the 5 plus 2 plus 3 letter word C’EST LA VIE
I've seen this crossword clue in Financial Times
C
â
€
™
E
S
T
L
A
V
I
E
More clues leading to the result C’EST LA VIE
Buddy explains!

The straight part
We know that "Resignation statement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case resignation statement = c’est la vie.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.