Extremely busy girl struggling with a piece of music (8)
I believe the answer is:
madrigal
'piece of music' is the definition.
(madrigal is a kind of piece of music)
'extremely busy girl struggling with a' is the wordplay.
'extremely busy' becomes 'mad' (mad can mean hectic or busy).
'struggling with' indicates an anagram (the letters struggle or wriggle into a new form).
'girl' with its letters anagrammed with 'a' can make 'rigal'.
'mad'+'rigal'='MADRIGAL'
(Other definitions for madrigal that I've seen before include "glee" , "air" , "Drag Liam around to hear an unaccompanied song" , "Without exaggeration" , "Old part song" .)