Last European quits modest protest (5)

I believe the answer is:

demur

'protest' is the definition.
(thesaurus)

I can't explain the remainder of the clue.

(Other definitions for demur that I've seen before include "Cavil, dispute" , "Protest mildly, show reluctance" , "Hesitate from uncertainty or object" , "'Object, show reluctance (5)'" , "Raise scruples" .)

I've seen this clue in The Guardian.

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