Extremely strict girl cracking joke (7)

I believe the answer is:

puritan

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

'extremely strict' is the definition.
'puritan' can be an answer for 'strict' (thesaurus). I am not sure about the 'extremely' bit.

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for puritan that I've seen before include "One forgoing pleasure" , "Member of a group of English Protestants who thought that the Protestant Reformation was incomplete" , "Dour Protestant" , "Prude" , "Moralistic type" .)

I've seen this clue in The Times and The Sunday Times.

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