Study onset of terrible depression (4)
I believe the answer is:
dent
'depression' is the definition.
('dent' can be a synonym of 'depression')
'study onset of terrible' is the wordplay.
'study' becomes 'den' (I've seen this before).
'onset of' says to take the initial letters.
The first letter of 'terrible' is 't'.
'den'+'t'='DENT'
(Other definitions for dent that I've seen before include "Hollow from impact" , "Tend to small indentation" , "A cavity" , "Mark of knock" , "Depression caused by blow" .)