Time spent by group playing big city (3)
I believe the answer is:
rio
'big city' is the definition.
'time spent by group playing' is the wordplay.
'time' becomes 't'.
'spent by' indicates named letters should be taken away.
'group playing' becomes 'trio' (musical group).
'trio' with 't' taken away is 'RIO'.
(Other definitions for rio that I've seen before include "place of carnival" , "Brazilian city and port" , "A Mexican river, may be grande" , "Flying Down to -, Astaire, Rogers film" , "Port, -- de Janeiro" .)