Crossword Genius

Incarcerate to prevent further speeches? (4,2)

Ross

I believe the answer is:

shut up

I'm a little stuck... Click here to teach me more about this clue!

'incarcerate' is the definition.
(thesaurus)

'to prevent further speeches?' is the wordplay.
I cannot quite see how this works, but
'to' could be 'shut' (I've seen this before) and 'shut' is located in the answer.
The remaining letters 'up' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for shut up that I've seen before include "Enclose; be quiet!" , "Button it!" , "jail" , "Hold your tongue" , "Rude order to stop speaking" .)

I've seen this clue in the Evening Standard.
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