Lives, I see, in cooler Iranian city (7)

I believe the answer is:

isfahan

'iranian city' is the definition.
(city in Iran)

'lives i see in cooler' is the wordplay.
'lives' becomes 'is' ('be' can be a synonym of 'live').
'i see' becomes 'ah' (exclamation used to indicate understanding).
'in' indicates putting letters inside.
'cooler' becomes 'fan' (I've seen this in another clue).
'ah' put inside 'fan' is 'fahan'.
'is'+'fahan'='ISFAHAN'

(Another definition for isfahan that I've seen is " Iranian city".)

I've seen this clue in The Times.

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