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Give a different order to retailer about keeping shtum (7)

Ross

I believe the answer is:

permute

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'retailer about keeping shtum' is the definition.
I can't tell whether this definition defines the answer.

'give a different order' is the wordplay.
'give' says to put letters next to each other.
'a' becomes 'per' (eg 'one a day' means 'one per day').
'different order' becomes 'mute' (I am not sure about this - if you are sure you should believe this answer much more).
'per' put next to 'mute' is 'PERMUTE'.

'to' acts as a link.

Can you help me to learn more?

(Other definitions for permute that I've seen before include "Shuffle order of" , "Rearrange" , "Change sequence of" .)

I've seen this clue in The Times.
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