Deeply disturb small milliner (7)

I believe the answer is:

shatter

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'deeply disturb' is the definition.
'shatter' can be an answer for 'disturb' (thesaurus). I am not certain of the 'deeply' bit.

'small milliner' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'milliner' becomes 'hatter' (synonyms).
's'+'hatter'='SHATTER'

Can you help me to learn more?

(Other definitions for shatter that I've seen before include "Break into many bits" , "total" , "Break into many pieces" , "Crack" , "Break suddenly" .)

I've seen this clue in The Guardian.

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