They're handled by besom makers (5)
I believe the answer is:
'makers' is the definition.
Although both the answer and definition are plural nouns, I can't see how one could define the other.
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for twigs that I've seen before include "Kindling" , "Understands" , "Small branches" , "Catches on" , "Slender woody shoots" .)