Stick taken across river for bird (5)
I believe the answer is:
crane
'for 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' is an insertion indicator.
'river' becomes 'r' (abbreviation).
'cane' enclosing 'r' is 'CRANE'.
(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" .)