Barber will take care of this musical (4)
I believe the answer is:
hair
This could be a double definition.
'barber' is the first definition.
(I've seen this in another clue)
'take care of this musical' is the second definition.
'hair' can be an answer for 'musical' (1960s musical). I am not certain of the rest of the definition.
'will' is the link.
Can you help me to learn more?
(Other definitions for hair that I've seen before include "Hirsute hippy musical with song 'aquarius'" , "One's crowning glory?" , "Musical with nude scenes" , "A very small quantity" , "Stage musical" .)