Melodious line absorbing hearts in variety entertainment (5,4)
I believe the answer is:
music hall
'variety entertainment' is the definition.
(I know that music hall is a type of variety entertainment)
'melodious line absorbing hearts' is the wordplay.
'melodious' becomes 'musical' (synonyms).
'line' becomes 'l' (used when specifying particular lines from a poem).
'absorbing' means one lot of letters goes inside another.
'hearts' becomes 'h' (abbreviation used in card games e.g. bridge).
'musical'+'l'='musicall'
'musicall' enclosing 'h' is 'MUSIC-HALL'.
'in' is the link.
(Other definitions for music hall that I've seen before include "Mainly C 19 variety entertainment" , "Vaudeville" , "A Palace of Varieties" , "A place for variety" , "Late 19th century entertainment, and the theatre it took place in" .)