Company's first musical furniture (5)
I believe the answer is:
chair
'furniture' is the definition.
(I know that chair is a type of furniture)
'company's first musical' is the wordplay.
'company's first' becomes 'c' (1st letter of 'company').
'musical' becomes 'hair' (1960s musical).
'c'+'hair'='CHAIR'
(Other definitions for chair that I've seen before include "Seat for one person" , "academic office" , "Professoriate" , "Preside over - seat" , "Single seat" .)