Lennon music regularly banished boredom (5)
I believe the answer is:
ennui
'boredom' is the definition.
(I know that boredom can be written as ennui)
'lennon music regularly banished' is the wordplay.
'regularly banished' indicates alternate letters (letters removed at regular intervals).
'lennon'+'music'='lennonmusic'
The alternating letters of 'lennonmusic' are 'ENNUI'.
(Other definitions for ennui that I've seen before include "What's tedious and instils such listlessness" , "Result of boredom" , "The feeling of being bored" , "Bored listlessness" , "Feeling of weariness or boredom" .)