Suddenly see part of a tree! (4)
I believe the answer is:
twig
I believe this is a double definition.
'suddenly see' is the first definition.
(I've seen this before)
'part of a tree' is the second definition.
(I've seen this before)
(Other definitions for twig that I've seen before include "Eventually grasp" , "Suddenly get" , "Small piece of wood" , "A little stick" , "Slender woody shoot" .)