Completely insensitive (4)

I believe the answer is:

dead

I believe this is a double definition.

'completely' is the first definition.
('dead' can be a synonym of 'completely')

'insensitive' is the second definition.
(thesaurus)

(Other definitions for dead that I've seen before include "cold" , "Lifeless" , "dull" , "Insensitive" , "Absolutely" .)

I've seen this clue in the Evening Standard.

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