A specialised threadlike leaf or stem that attaches climbing plants to a support by twining or adhering (7)
I believe the answer is:
tendril
(Other definitions for tendril that I've seen before include "Threadlike extension of a plant" , "Natural thread climbing plants produce to attach to a support" , "Climbing plant's grasper" , "Climbing plant's supporter" , "Stem by which climbing plant attaches itself" .)