One news supremo quickly on the rise in City (8)
I believe the answer is:
pasadena
'city' is the definition.
(Pasadena is a city in California)
'one news supremo quickly on the rise' is the wordplay.
'one' becomes 'an' (an apple is one apple).
'news supremo' becomes 'ed' (editor, newspaper boss).
'quickly' becomes 'asap' (as soon as possible).
'on the rise' is a reversal indicator (in a down clue, letters go up).
'an'+'ed'+'asap'='anedasap'
'anedasap' backwards is 'PASADENA'.
'in' is the link.
(Other definitions for pasadena that I've seen before include "City in Los Angeles County" , "California city of the Rose Bowl stadium" , "Californian city" , "US city" , "place in California" .)