A hairy operation (tonsorial) (5)

I believe the answer is:

singe

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'a hairy operation' is the definition.
The definition and answer can be both states of affairs as well as being singular nouns.
Maybe you can see an association between them that I don't see?

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for singe that I've seen before include "Burn superficially" , "slight burn" , "Sear" , "Result of match accident" , "Burn the ends or edges of" .)

I've seen this clue in the Evening Standard.

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