It’s not entirely sunk in: destitute and extremely cold (9)

I believe the answer is:

unkindest

'extremely cold' is the definition.
(unkind to an extreme degree)

'it's not entirely sunk in destitute' is the wordplay.
'it's not entirely' indicates the answer is hidden within the clue.
'UNKINDEST' can be found hidden inside 'sunk in destitute'.

'and' acts as a link.

(Other definitions for unkindest that I've seen before include "Extremely cruel" , "Most uncharitable" , "Most brutal" .)

I've seen this clue in The Times.

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