Check river in Hampshire (4)
I believe the answer is:
test
This clue is a double definition.
'check' is the first definition.
(as in testing or checking something works)
'river in hampshire' is the second definition.
(the River Test flows through Hampshire)
(Other definitions for test that I've seen before include "Trial; Hampshire river" , "Check" , "Sample" , "Short exam" , "big game" .)