Broadcasting one short melody (2,3)
I believe the answer is:
on air
'broadcasting' is the definition.
(broadcasting on the air)
'one short melody' is the wordplay.
'short' means to remove the last letter.
'melody' becomes 'air' (synonyms).
'one' with its last letter taken off is 'on'.
'on'+'air'='ON AIR'
(Other definitions for on air that I've seen before include "Walk in delight here" , "Broadcasting studio sign" , "Broadcasting at this moment" , "now showing" , "(Walking) elatedly" .)