Atmosphere by far side of the river (4)
I believe the answer is:
aire
'river' is the definition.
(I've seen this before)
'atmosphere by far side of the' is the wordplay.
'atmosphere' becomes 'air' ('air' can be a synonym of 'atmosphere'**).
'by' means one lot of letters go next to another.
'far side of' suggests the final letters.
The final letter of 'the' is 'e'.
'air'+'e'='AIRE'
(Other definitions for aire that I've seen before include "River running through Leeds" , "Terrier -- Yorkshire area" , "English flower" , "River of the Yorkshire dales" , "flower of Yorkshire" .)