Composer wanting end mostly minor (7)

I believe the answer is:

tippett

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'composer' is the definition.
(I've seen this before)

'wanting end mostly minor' is the wordplay.
'wanting end' becomes 'tip' (tip is a kind of end. I am not sure about the 'wanting' bit.).
'mostly' means to remove the last letter (most but not all of the word).
'minor' becomes 'petty' (I've seen this in another clue).
'petty' with its final letter taken away is 'pett'.
'tip'+'pett'='TIPPETT'

Can you help me to learn more?

(Another definition for tippett that I've seen is " Sir Michael -, English composer".)

I've seen this clue in The Times.

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