Terribly inane musical (5)
I believe the answer is:
annie
'musical' is the definition.
(Annie is a Broadway musical)
'terribly inane' is the wordplay.
'terribly' indicates anagramming the letters.
'inane' is an anagram of 'ANNIE'.
(Other definitions for annie that I've seen before include "Little Ophan .....; also a musical" , "girl instructed to get gun" , "Inane (anag) - girl (with a gun?)" , "-- Lennox, singer" , "1977 Broadway musical" .)