Crossword Genius

Bishop managed church office locally (6)

Ross

I believe the answer is:

branch

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'office locally' is the definition.
I can't tell whether this definition defines the answer.

'bishop managed church' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'managed' becomes 'ran' (both can mean organised or was in charge of).
'church' becomes 'ch' (common abbreviation).
'b'+'ran'+'ch'='BRANCH'

Can you help me to learn more?

(Other definitions for branch that I've seen before include "regional office" , "Bough - offshoot - secondary office" , "Lateral extension of river or railway" , "local office" , "Part of tree/river" .)

I've seen this clue in The Times.
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