The most common and most likely answer to this crossword clue is the 5 plus 3 letter word HISSY FIT
I've seen this crossword clue in Financial Times
H
I
S
S
Y
F
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T
More clues leading to the result HISSY FIT
- Petulant display at sea is shifty
- In a tizzy, is this fury in the extreme?
- Is shy changing suit? Tantrum results
- Fellow’s extremely silly suit leads to outburst
- Pervert is shifty and having a tantrum
- Is shy, after misbehaving with proper tantrum
- Is shy after misbehaving with proper tantrum
- If this shakes about scarily at the sides, it's wobbly
- Pet is shy around mate
- Is shy, awkward, before proper temper tantrum
Buddy explains!

The straight part
We know that "outburst" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case outburst = hissy fit.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.