I'm in Los Angeles, that great city (4)

I believe the answer is:

lima

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'great city' is the definition.
'lima' can be an answer for 'city' (Lima is an example). I'm not sure about the 'great' bit.

'i'm in los angeles' is the wordplay.
'i'm' becomes 'im' ().
'in' is an insertion indicator.
'los angeles' becomes 'LA' (abbreviation).
'im' going inside 'la' is 'LIMA'.

'that' is the link.

Can you help me to learn more?

(Other definitions for lima that I've seen before include "Edible bean; capital city" , "Send mail out to S America" , "Mail it to Peruvian city" , "Kind of bean" , "Peruvian capital" .)

I've seen this clue in the Evening Standard.

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