13 across
Administrative
division
or
dividing
branch
(7)
Administrative division or dividing branch (7)
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The definition is at the beginning of the clue.
How the clue works
The definition is Administrative division — a borough being a type of administrative district. Then or dividing branch gives you the wordplay: take bough (branch) and split it with or sitting inside, giving you B, then OR, then OUGH.