Happily sing choral composition that's not hard (5)

I believe the answer is:

carol

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'happily sing' is the definition.
'carol' can be an answer for 'sing' (caroling is a kind of singing). I'm unsure of the 'happily' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for carol that I've seen before include "Song, especially at Christmas" , "Religious song - girl's name" , "A traditional Christmas song or hymn" , "Canticle" , "Female" .)

I've seen this clue in the Independent.

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