Bird getting lower circling river (4)
I believe the answer is:
crow
'bird' is the definition.
(crow is a kind of bird)
'lower circling river' is the wordplay.
'lower' becomes 'cow' (**).
'circling' indicates putting letters inside (circling can mean going around or containing).
'river' becomes 'r'.
'cow' going around 'r' is 'CROW'.
'getting' acts as a link.
(Other definitions for crow that I've seen before include "Ugly old woman" , "Blow one's own trumpet" , "Bird in 1's poems" , "one often getting stoned!" , "Black bird with raucous call" .)