Crossword Genius

Elite soldiers quickly finding hairdresser (7)

Ross

I believe the answer is:

sassoon

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'hairdresser' is the definition.
Both the answer and definition are singular nouns.
Perhaps they are linked in a way I don't understand?

'elite soldiers quickly' is the wordplay.
'elite soldiers' becomes 'sas' (Special Air Service).
'quickly' becomes 'soon' (I've seen this in another clue).
'sas'+'soon'='SASSOON'

'finding' acts as a link.

Can you help me to learn more?

(Other definitions for sassoon that I've seen before include "Siegfried --, English poet and novelist" , "Siegfried --, English writer" , "Siegfried ---, war poet" , "Poet condemning war" , "Siegfried --, poet and writer" .)

I've seen this clue in The Sun.
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