Rarer stigma before Church elder, finally (7)

I believe the answer is:

scarcer

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'rarer' is the definition.
Both the definition and answer are comparative adjectives. Perhaps they are linked in a way I don't understand?

'stigma before church elder finally' is the wordplay.
'stigma' becomes 'scar' (I've seen this before).
'before' means one lot of letters go next to another.
'church' becomes 'CE' (Church of England).
'finally' says to take the final letters.
The final letter of 'elder' is 'r'.
'scar'+'ce'+'r'='SCARCER'

Can you help me to learn more?

(Other definitions for scarcer that I've seen before include "Less common" , "More unusual" , "More rare" .)

I've seen this clue in The Telegraph.

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