Promise to be quiet throughout (5)

I believe the answer is:

shall

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'promise' is the definition.
The answer and definition can be both to do with fundamental existence as well as being verbs in their base form.
Maybe they are linked in a way I don't understand?

'quiet throughout' is the wordplay.
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'throughout' becomes 'all' (I can't justify this - if you can you should believe this answer much more).
'sh'+'all'='SHALL'

'to be' acts as a link.

Can you help me to learn more?

(Other definitions for shall that I've seen before include "' - - We Dance?'" , "Will, must, is to" .)

I've seen this clue in The Independent.

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