Stick taken across river for bird (5)
I believe the answer is:
crane
'bird' is the definition.
(crane is a kind of bird)
'stick taken across river' is the wordplay.
'stick' becomes 'cane' (cane is a kind of stick).
'taken across' indicates putting letters inside.
'river' becomes 'r' (abbreviation).
'cane' enclosing 'r' is 'CRANE'.
'for' is the link.
(Other definitions for crane that I've seen before include "Large long-legged bird" , "Lifting structure" , "Device for picking up" , "Bird; camera platform" , "Bird; dockside machine" .)