Appearing embarrassed by colour of Holmes’s study (7)

I believe the answer is:

scarlet

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'appearing embarrassed by colour' is the definition.
'scarlet' can be an answer for 'colour' (scarlet is a kind of colour). I am unsure of the 'appearing embarrassed by' bit.

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for scarlet that I've seen before include "Let cars be this colour" , "Cartels (anag.)" , "Red colour of clarets" , "Bright red of clarets" , "Fallen" .)

I've seen this clue in The Times.

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