Set of individual duties and responsibilities initially rejected (5)
I believe the answer is:
radio
'set' is the definition.
(set can mean a radio set)
'of individual duties and responsibilities initially rejected' is the wordplay.
'initially' indicates taking the first letters.
'rejected' shows that the letters should be reversed in order.
The first letters of 'of individual duties and responsibilities' is 'oidar'.
'oidar' in reverse letter order is 'RADIO'.
(Other definitions for radio that I've seen before include "Part of the broadcasting industry" , "Receiving device" , "Transmitter" , "Transmit" , "Transistor" .)