It beats a bit of a beard (7)
I believe the answer is:
whisker
'beard' is the definition.
(thesaurus)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for whisker that I've seen before include "Long facial hair" , "Sensory hair of a cat" , "Hair on cat's face" , "narrow margin" , "Hair's breadth" .)