A mate raised middle child in Middle East city (5)

I believe the answer is:

dubai

I'm a little stuck... Click here to teach me more about this clue!

'middle east city' is the definition.
'dubai' can be an answer for 'city' (UAE city). I am not certain of the 'middle east' bit.

'a mate raised middle child' is the wordplay.
'mate' becomes 'bud' (shortly for buddy).
'raised' is a reversal indicator (going up in a down clue).
'middle' means to look at the middle letters.
The middle of 'child' is 'i'.
'a'+'bud'='abud'
'abud' reversed gives 'duba'.
'duba'+'i'='DUBAI'

'in' is the link.

Can you help me to learn more?

(Other definitions for dubai that I've seen before include "Middle East destination" , "Port city on the Persian Gulf" , "Country" , "Gulf city/state" , "Port city of UAE" .)

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

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