Quiet - that's the way to listen! (6)

I believe the answer is:

silent

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'quiet' is the definition.
(similar in meaning)

'the way to listen' is the wordplay.
'listen' anagrams to 'SILENT'.
However, I'm unsure how the anagram is indicated.

'that's' is the link.

Can you help me to learn more?

(Other definitions for silent that I've seen before include "Dumb" , "Not speaking" , "Unheard" , "Without sound" , "Refusing to communicate" .)

I've seen this clue in the Evening Standard.

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