Puritan to turn on leader (9)

I believe the answer is:

roundhead

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'puritan' is the definition.
The definition and answer can be both people as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'turn on leader' is the wordplay.
'turn on' becomes 'round' (synonyms. I am not sure about the 'on' bit.).
'leader' becomes 'head' (head is a kind of leader).
'round'+'head'='ROUNDHEAD'

'to' is the link.

Can you help me to learn more?

(Other definitions for roundhead that I've seen before include "antimonarchist" , "Supporter of Parliament during the English Civil Wars" , "Old soldier" , "Cavalier's foe" , "Parliamentarian (hist.)" .)

I've seen this clue in the Sydney Morning Herald.

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