Old musical that needs regular cutting? (4)

I believe the answer is:

hair

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'old musical' is the definition.
'hair' can be an answer for 'musical' (1960s musical). I'm not certain of the 'old' bit.

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for hair that I've seen before include "Barber's speciality; musical" , "The American Tribal Love-Rock Musical (1967)" , "Showy garden flower" , "Threadlike strands growing from the skin" , "Fibre; small extent" .)

I've seen this clue in The Times.

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