Leave out what's upsetting in testimony (4)
I believe the answer is:
omit
'leave out' is the definition.
('omit' can be a synonym of 'leave out')
'upsetting in testimony' is the wordplay.
'upsetting' says the letters should be written in reverse.
'in' indicates a hidden word.
'timo' is hidden in the letters of 'testimony'.
'timo' reversed gives 'OMIT'.
'what's' acts as a link.
(Other definitions for omit that I've seen before include "Leave out, perhaps in error" , "Leave out or forget" , "Leave out or overlook" , "Neglect to include" , "Exclude; veto" .)