Study onset of tropical depression (4)
I believe the answer is:
dent
'depression' is the definition.
('dent' can be a synonym of 'depression')
'study onset of tropical' is the wordplay.
'study' becomes 'den' (I've seen this before).
'onset of' suggests taking the first letters.
The first letter of 'tropical' is 't'.
'den'+'t'='DENT'
(Other definitions for dent that I've seen before include "Surface hollow" , "Arthur, described by Douglas" , "TV lexicographer?" , "northern banker" , "Hollow caused by a blow" .)