The most common and most likely answer to this crossword clue is the 3 plus 1 plus 5 plus 5 letter word NOT A HAPPY BUNNY
N
O
T
A
H
A
P
P
Y
B
U
N
N
Y
More clues leading to the result NOT A HAPPY BUNNY
Buddy explains!

The straight part
We know that "dissatisfied person" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dissatisfied person = not a happy bunny.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.