The most common and most likely answer to this crossword clue is the 6 letter word SHOCKS
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "Hairy things/upsets" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hairy things/upsets = shocks.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.
What does SHOCKS mean?
SHOCKS noun- A sudden, heavy impact.
- A discontinuity arising in the solution of a partial differential equation.
- To cause to be emotionally shocked, to cause (someone) to feel surprised and upset.
- To give an electric shock to.
- To meet with a shock; to collide in a violent encounter.
- An arrangement of sheaves for drying; a stook.
- A lot consisting of sixty pieces; a term applied in some Baltic ports to loose goods.
- (by extension) A tuft or bunch of something, such as hair or grass.
- A small dog with long shaggy hair, especially a poodle or spitz; a shaggy lapdog.
- To collect, or make up, into a shock or shocks; to stook.