Got the doctor for those in rundown part of the city (6)

I believe the answer is:

ghetto

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'the city' is the definition.
(thesaurus)

'got the doctor' is the wordplay.
'doctor' indicates anagramming the letters.
'got'+'the'='gotthe'
'gotthe' is an anagram of 'GHETTO'.

'for those in rundown part of' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for ghetto that I've seen before include "poor part of town" , "Needy part of city" , "Ethic quarter" , "Segregated part of city for minority" , "Historical Jewish quarter" .)

I've seen this clue in The Irish Times and the Irish Times (Crosaire).

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