Network's first to plug old tune that's being broadcast (2,3)
I believe the answer is:
on air
'being broadcast' is the definition.
(on air on radio or TV)
'network's first to plug old tune' is the wordplay.
'network's first' becomes 'n' (1st letter of 'network').
'to plug' means one lot of letters goes inside another (to plug can mean to block a gap within something).
'old' becomes 'o' (abbreviation).
'tune' becomes 'air' (air can mean a piece of music).
'o'+'air'='oair'
'n' inserted within 'oair' is 'ON-AIR'.
'that's' is the link.
(Other definitions for on air that I've seen before include "Currently broadcasting" , "Transmitting now!" , "Broadcasting live" , "In the act of broadcasting" , "How one walks when elated" .)