Become weary of Green (4)
I believe the answer is:
jade
I believe this is a double definition.
'become weary' is the first definition.
(I've seen this in another clue)
'green' is the second definition.
(I know that jade is a type of green)
'of' is the link.
(Other definitions for jade that I've seen before include "weary" , "Ornamental semiprecious stone" , "Green gemstone" , "Green gem" , "Mount" .)