… beginning to smoke a chillum (new variety) (5,4)
I believe the answer is:
music hall
'variety' is the definition.
(I know this)
'beginning to smoke a chillum new' is the wordplay.
'beginning to' suggests taking the first letters.
'new' indicates an anagram.
The first letter of 'smoke' is 's'.
's'+'a'+'chillum'='sachillum'
'sachillum' is an anagram of 'MUSIC-HALL'.
(Other definitions for music hall that I've seen before include "Late 19th century entertainment, and the theatre it took place in" , "Mainly C 19 variety entertainment" , "A Palace of Varieties" , "A place for variety" , "Vaudeville" .)