Crossword Genius

Reporters caught her in this part of town (7)

Ross

I believe the answer is:

quarter

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'reporters caught her in this part of town' is the definition.
'quarter' can be an answer for 'part' (quarter is a kind of part). I am unsure of the rest of the definition.

'part of town' is the wordplay.
I cannot really understand how this works, but
'part' could be 'te' (te is a kind of part) and 'te' is found within the answer.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for quarter that I've seen before include "Lodge" , "Mercy; fraction" , "Fourth; part of town" , "A small piece" , "Area of town; mercy" .)

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