Rule by three score about one bridge (8)

I believe the answer is:

triarchy

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'rule by three' is the definition.
The definition suggests a singular noun which matches the answer.

'score about one bridge' is the wordplay.
'score' becomes 'try' ().
'about' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'bridge' becomes 'arch' (I've seen this before).
'i'+'arch'='iarch'
'try' going around 'iarch' is 'TRIARCHY'.

Can you help me to learn more?

(Other definitions for triarchy that I've seen before include "ruling three" , "Three-man government" .)

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

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