Modest, but sounding much in demand? (6)

I believe the answer is:

chaste

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'modest' is the definition.
(I've seen this before)

I cannot understand how the rest of the clue works.

(Other definitions for chaste that I've seen before include "Pure and decent" , "Showing virtue of kind" , "Modest and decent" , "Modest, pure" , "Decorous" .)

I've seen this clue in The Times.

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