Four dropping out of unimportant Test (5)
I believe the answer is:
trial
'test' is the definition.
('trial' can be a synonym of 'test')
'four dropping out of unimportant' is the wordplay.
'four' becomes 'iv' ('IV' can be a synonym of 'four').
'dropping out of' indicates named letters should be taken away.
'unimportant' becomes 'trivial' ('trivial' can be similar in meaning to 'unimportant').
'trivial' with 'iv' taken out is 'TRIAL'.
(Other definitions for trial that I've seen before include "French actor who sings" , "Legal proceedings or a test run" , "Troublesome thing; test" , "Ordeal, perhaps in court" , "show at Crufts?" .)