Clinton's issue with part of London (7)

I believe the answer is:

chelsea

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'part of london' is the definition.
'chelsea' can be an answer for 'part' (I have seen 'Part of Manhattan' mean 'chelsea' so perhaps 'part' could also mean 'chelsea'). I'm not sure about the 'of london' bit.

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for chelsea that I've seen before include "Part of our capital" , "Team in blue" , "London football team" , "Lace she found in London area" , "Part of Manhattan" .)

I've seen this clue in The Independent.

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