Crossword Genius

A bishop meets old church music composer who is teetotal? (9)

Ross

I believe the answer is:

abstainer

I'm a little stuck... Click here to teach me more about this clue!

'composer who is teetotal?' is the definition.
The definition and answer can be both people as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'a bishop meets old church music' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'meets' means one lot of letters go next to another.
'old church music' becomes 'stainer' (I can't justify this - if you can you should believe this answer much more).
'a'+'b'+'stainer'='ABSTAINER'

Can you help me to learn more?

(Other definitions for abstainer that I've seen before include "Non-drinker" , "AA member" , "One choosing not to vote" , "One refusing hard stuff" , "Rechabite" .)

I've seen this clue in The Guardian.
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