Cover needed when the medico is hors de combat (4)

I believe the answer is:

coat

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'cover' is the definition.
(I know that coat is a type of hair)

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

(Other definitions for coat that I've seen before include "Outer covering" , "Jacket" , "Fleece" , "Overgarment" , "Ulster, perhaps" .)

I've seen this clue in the Evening Standard.

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