One’s obliged by old townsperson to be silent (5)

I believe the answer is:

tacit

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'silent' is the definition.
(I know that silent can be written as tacit)

I don't understand the remainder of the clue.

(Other definitions for tacit that I've seen before include "Wordless" , "Silent but implied" , "Understood without being directly expressed" , "Implied but not directly expressed" , "Respect, admiration" .)

I've seen this clue in The Times.

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