Independent's right to plug Guardian's listening device (4)
I believe the answer is:
wire
'listening device' is the definition.
'independent's right to plug guardian's' is the wordplay.
'independent' becomes 'i'.
'right' becomes 'r' (common abbreviation).
'to plug' is an insertion indicator (to plug can mean to block a gap within something).
'guardian's' becomes 'we' (I am not sure about this - if you are sure you should believe this answer much more).
'i'+'r'='ir'
'ir' inserted into 'we' is 'WIRE'.
(Other definitions for wire that I've seen before include "Thin drawn metal" , "Hand signal; breaker" , "See 20" , "Strand of metal" , "Thin metal thread" .)