Game leader departing with a word of appreciation in Asian city, once (4-3)

'asian city once' is the definition.
(former spelling for Almaty)

'game leader departing with a word of appreciation' is the wordplay.
'game' becomes 'halma' (board game).
'leader departing' means to remove the first letter.
'with' becomes 'a' (I can't explain this - if you can you should give a lot more credence to this answer).
'a word of appreciation' becomes 'ta' (UK informal way of saying 'thank you').
'halma' with its first letter removed is 'alma'.
'alma'+'a'+'ta'='ALMA-ATA'

'in' acts as a link.