Pursued it's said but completely virtuous (6)

I believe the answer is:

chaste

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'completely virtuous' is the definition.
'chaste' can be an answer for 'virtuous' (associated in meaning). I am not sure about the 'completely' bit.

'pursued it's said' is the wordplay.
'pursued' becomes 'chased' (synonyms).
'it's said' shows a homophone (sound like).
'chased' is a homophone of 'CHASTE'.

'but' acts as a link.

Can you help me to learn more?

(Other definitions for chaste that I've seen before include "Decorous" , "Sexually virtuous" , "pure and simple" , "Maidenly" , "Morally pure" .)

I've seen this clue in The Globe and Mail.

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