Game leader departing with a word of appreciation in Asian city, once (4-3)
I believe the answer is:
Here is my best explanation:
'asian city once' is the definition.
(former spelling for Almaty)
'game leader departing with a word of appreciation' is the subsidiary indication.
'game' becomes 'alma' (I can't justify this - if you can you should give a lot more credence to this answer).
'leader departing' means to remove the first letter.
'with' becomes 'w' (abbreviation).
'word of appreciation' becomes 'ta' (UK informal way of saying 'thank you').
'wa' with its initial letter taken away is 'a'.
'in' is the link.
(Another definition for alma-ata that I've seen is "Former capital city in Kazakhstan".)