Terribly idle around hot Asian city (5)
I believe the answer is:
delhi
'asian city' is the definition.
(New Delhi)
'terribly idle around hot' is the wordplay.
'terribly' indicates anagramming the letters.
'around' means one lot of letters goes inside another.
'hot' becomes 'h' (abbreviation eg on taps).
'idle' with letters rearranged gives 'deli'.
'deli' placed around 'h' is 'DELHI'.
(Other definitions for delhi that I've seen before include "Indian territory" , "Indian state" , "Ancient city" , "It's also new in India" , "Capital on the river Jumna" .)