Award goes to old city dome (6)
I believe the answer is:
cupola
'dome' is the definition.
(I know that cupola is a type of dome)
'award goes to old city' is the wordplay.
'award' becomes 'cup' (I've seen this in other clues).
'goes to' is a charade indicator (letters next to each other).
'old' becomes 'o' (abbreviation).
'city' becomes 'LA' (Los Angeles).
'cup'+'o'+'la'='CUPOLA'
(Other definitions for cupola that I've seen before include "fireplace" , "Round domed roof" , "Dome - furnace" , "Rounded dome" , "St Peter's roof" .)