Set a date, initially in South American city (5)
I believe the answer is:
radio
'set' is the definition.
(radio is a kind of set)
'a date initially in south american city' is the wordplay.
'initially' says to take the initial letters.
'in' indicates putting letters inside.
'south american city' becomes 'rio' (I've seen this before).
The first letter of 'date' is 'd'.
'a'+'d'='ad'
'ad' inserted into 'rio' is 'RADIO'.
(Other definitions for radio that I've seen before include "Broadcast receiver" , "Communications receiver" , "It used to be called the wireless" , "Transmitter" , "Sound receiver" .)