Former prison's innovative entrance (7)

I believe the answer is:

newgate

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

'former prison's' is the definition.
'Newgate' can be an answer for 'prison's' (I've seen this before). I am not sure about the 'former' bit.

'innovative entrance' is the wordplay.
'innovative' becomes 'new' (I've seen this in another clue).
'entrance' becomes 'gate' (type of entrance).
'new'+'gate'='NEWGATE'

Can you help me to learn more?

(Other definitions for newgate that I've seen before include "Old Nick" , "Notorious 18th-century London prison" , "London street" , "Stir in capital" , "Old London prison" .)

I've seen this clue in The Times.

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