Church musician upset his rector (9)

I believe the answer is:

chorister

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'church musician' is the definition.
'chorister' can be an answer for 'musician' (chorister is a kind of musician). I am not certain of the 'church' bit.

'upset his rector' is the wordplay.
'upset' indicates anagramming the letters.
'his'+'rector'='hisrector'
'hisrector' with letters rearranged gives 'CHORISTER'.

Can you help me to learn more?

(Other definitions for chorister that I've seen before include "Choir member" , "Boy singer" , "Boy singing" , "Church, cathedral singer" , "Choirboy or girl" .)

I've seen this clue in The Times.

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