One beats by a very short distance (7)
I believe the answer is:
whisker
This clue is a double definition.
'one beats' is the first definition.
(eg someone who beats or whisks an egg)
'a very short distance' is the second definition.
(whisker can mean a tiny distance or amount)
'by' acts as a link.
(Other definitions for whisker that I've seen before include "Hair on cat's face" , "Sensory hair of a cat" , "Long stiff hair, of a cat say" , "Hair's breadth" , "narrow margin" .)