Area mainly bounded inside territory, principally (5)

I believe the answer is:

ambit

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'area mainly bounded inside territory principally' is the definition.
I can't tell whether this definition defines the answer.

'area mainly bounded inside territory principally' is the wordplay.
'area' becomes 'a' (maths abbreviation).
'principally' says to take the initial letters.
The initial letters of 'mainly bounded inside territory' is 'mbit'.
'a'+'mbit'='AMBIT'

Can you help me to learn more?

(Other definitions for ambit that I've seen before include "Circumference" , "Compass, scope" , "round" , "Limits" , "Circuit, compass" .)

I've seen this clue in The Telegraph.

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