One river after another in the countryside (5)
I believe the answer is:
rural
'in the countryside' is the definition.
(rural means in the countryside)
'one river after another' is the wordplay.
'one river' becomes 'r' (abbreviation for river).
'after' says to put letters next to each other.
'another' becomes 'ural' (I can't explain this - if you can you should believe this answer much more).
'r'+'ural'='RURAL'
(Other definitions for rural that I've seen before include "Not urban" , "Countrified" , "Countrylike" , "Countryfied" , "Cobbett saw on his rides?" .)