Crossword Genius

Don't take out adequate insurance, being secretive (10)

Ross

I believe the answer is:

undercover

I'm a little stuck... Click here to teach me more about this clue!

'don't take out adequate insurance being secretive' is the definition.
I can't judge whether this defines the answer.

'out adequate insurance being secretive' is the wordplay.
I cannot quite understand how this works, but
'out' could be 'under' (I've seen this in another clue) and 'under' is present in the answer.
'insurance' could be 'cover' (I've seen this before) and 'cover' is located in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for undercover that I've seen before include "What spy may be" , "Secret (operations)" , "Hidden" , "Like incognito spy" , "How a book may be found" .)

I've seen this clue in The Irish Times.
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