Dip toe in Hampshire river (4)
I believe the answer is:
test
This clue is a double definition.
'dip toe in' is the first definition.
(as in testing the waters)
'hampshire river' is the second definition.
(River Test)
(Other definitions for test that I've seen before include "Short exam" , "Critical examination or trial of qualities or abilities" , "Exam to play international cricket" , "Dip one's toe in" , "Audition" .)