Crossword Genius

Practice of seeking to gain superiority over others (3-9)

Ross

I believe the answer is:

one-upmanship

(Other definitions for one-upmanship that I've seen before include "Art of showing off (Potter)" , "The art of maintaining an advantage over someone" , "(Stephen Potter's) art of keeping a jump ahead of competitor" , "Way of feeling superior to another" , "The art of gaining the advantage" .)

I've seen this clue in The Times.
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