Does like time pursuing friend in US city (8)

I believe the answer is:

budapest

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'us city' is the definition.
'Budapest' can be an answer for 'city' (Budapest is an example). I am not sure about the 'us' bit.

'does like time pursuing friend' is the wordplay.
'does like' becomes 'apes' (I've seen this in another clue).
'time' becomes 't' (abbreviation).
'pursuing' says to put letters next to each other.
'friend' becomes 'bud' (short for buddy).
'apes'+'t'='apest'
'apest' after 'bud' is 'BUDAPEST'.

'in' is the link.

Can you help me to learn more?

(Other definitions for budapest that I've seen before include "Hungarian capital" , "Capital city on the Danube" , "city of Europe" , "European capital" , "Ernest Laszlo's birthplace" .)

I've seen this clue in The Times.

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