Small jazz group touring most of old Asian capital (7)
I believe the answer is:
colombo
'asian capital' is the definition.
(capital of Sri Lanka)
'small jazz group touring most of old' is the wordplay.
'small jazz group' becomes 'combo' (combo can mean a jazz band).
'touring' means one lot of letters goes inside another (touring can mean going round).
'most of' means to remove the last letter.
'old' with its last letter taken away is 'ol'.
'combo' enclosing 'ol' is 'COLOMBO'.
(Other definitions for colombo that I've seen before include "Capital of Sri Lanka" , "Sri Lankan capital" , "City of Sri Lanka" , "Asian city" , "Sri Lankan port" .)