Insignia regularly provides hidden message in puzzles (4)

I believe the answer is:

nina

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'provides hidden message in puzzles' is the definition.
I can't tell whether this definition defines the answer.

'insignia regularly' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternate letters of 'insignia' are 'NINA'.

Can you help me to learn more?

(Other definitions for nina that I've seen before include "- - Simone, 1933-2003, singer" , "Al Hirschfeld's 'hidden' daughter" , "- Simone, US singer" , "One of Columbus's ships in 1492; girl's name" , "Girl" .)

I've seen this clue in The Irish Times.

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