Desensitise about a Norse broadcast (7)

I believe the answer is:

coarsen

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'desensitise' is the definition.
I can't tell whether this definition defines the answer.

'about a norse broadcast' is the wordplay.
'about' becomes 'c' (abbreviation for circa).
'broadcast' indicates anagramming the letters (letters scattered or cast around).
'a'+'norse'='anorse'
'anorse' with letters rearranged gives 'oarsen'.
'c'+'oarsen'='COARSEN'

Can you help me to learn more?

(Other definitions for coarsen that I've seen before include "Make rougher" , "Become rough or insensitive" , "Make rough or crude" , "Turn rough" , "Dull" .)

I've seen this clue in The Daily Express.

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