Golf club in the south of France Republican applied to (7)

I believe the answer is:

midiron

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'golf club' is the definition.
(I know that midiron is a type of golf club)

'south of france republican applied to' is the wordplay.
'south of france' becomes 'midi' ('Le Midi' is a French term for the south of France).
'republican' becomes 'ron' (I can't justify this - if you can you should believe this answer much more).
'applied to' is a charade indicator (letters next to each other).
'midi'+'ron'='MIDIRON'

'in the' acts as a link.

Can you help me to learn more?

(Another definition for midiron that I've seen is " golf club".)

I've seen this clue in The Times.

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