Running small broadcast leads to boredom (5)
I believe the answer is:
ennui
'to boredom' is the definition.
(synonyms)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for ennui that I've seen before include "depression" , "Boredom, listlessness" , "Low interest rate" , "The feeling of being bored" , "doldrums" .)