Hot show becomes a musical (4)
I believe the answer is:
hair
'a musical' is the definition.
(1960s musical)
'hot show' is the wordplay.
'hot' becomes 'h' (abbreviation eg on taps).
'show' becomes 'air' (both can mean broadcast).
'h'+'air'='HAIR'
'becomes' acts as a link.
(Other definitions for hair that I've seen before include "Barber's speciality; musical" , "A very small quantity" , "One's crowning glory?" , "Growth from skin" , "It grows from the skin" .)