Gloat, getting farm animal across river (4)
I believe the answer is:
crow
'gloat' is the definition.
(I know that gloat can be written as crow)
'farm animal across river' is the wordplay.
'farm animal' becomes 'cow' (type of farm animal).
'across' means one lot of letters goes inside another.
'river' becomes 'r' (abbreviation for river).
'cow' placed around 'r' is 'CROW'.
'getting' is the link.
(Other definitions for crow that I've seen before include "Ugly old woman" , "Make sounds of pleasure as a baby does - or a bird" , "Brag; carrion bird" , "One joins others in a murder" , "'As the - - flies'" .)