Cunning, having Crete altered in a hidden way (8)

I believe the answer is:

secretly

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'in a hidden way' is the definition.
I can't judge whether this defines the answer.

'cunning having crete altered' is the wordplay.
'cunning' becomes 'sly' (synonyms).
'having' is an insertion indicator.
'altered' indicates an anagram.
'crete' is an anagram of 'ecret'.
'sly' placed around 'ecret' is 'SECRETLY'.

Can you help me to learn more?

(Other definitions for secretly that I've seen before include "under the counter" , "On the quiet" , "On the q.t" , "privately" , "in disguise?" .)

I've seen this clue in The Daily Express.

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