Beastly noise by river in a desolate place (4)
I believe the answer is:
moor
'a desolate place' is the definition.
(I've seen this in another clue)
'beastly noise by river' is the wordplay.
'beastly noise' becomes 'moo' (I've seen this in another clue).
'by' means one lot of letters go next to another.
'river' becomes 'r' (abbreviation for river).
'moo'+'r'='MOOR'
'in' acts as a link.
(Other definitions for moor that I've seen before include "Secure boat with ropes" , "Heathery upland" , "Expanse of uncultivated upland" , "Open upland; tie up boat" , "The Battle of Marston - -" .)