Gift of composer capturing the essence of music (7)
I believe the answer is:
Here is my best explanation:
'gift' is the definition.
(I have seen 'traditional gift' mean 'handsel' so perhaps 'gift' could also mean 'handsel')
'composer capturing the essence of music' is the subsidiary indication.
'composer' becomes 'handel' (Handel is an example**).
'capturing' indicates putting letters inside.
'the essence of' says to take the centre.
The middle letters of 'music' are 's'.
'handel' going around 's' is 'handsel'.
'of' is the link.
(Other definitions for handsel that I've seen before include "A present for good luck, sealing of a bargain", "gift yesterday", "Might she land a good luck present?", "traditional gift", "Fairytale character" and "A good-luck present, coin in a purse, say".)