Try some private study (4)
I believe the answer is:
test
'try' is the definition.
(I know that try can be written as test)
'some private study' is the wordplay.
'some' indicates a hidden word (some parts of the word are used).
'TEST' can be found hidden inside 'private study'.
(Other definitions for test that I've seen before include "Check" , "Evaluation" , "Analyse" , "Cricket match; exam" , "Experiment" .)