Leaves out part of testimony when sent back (5)
I believe the answer is:
omits
'leaves out' is the definition.
('omit' can be a synonym of 'leave out')
'part of testimony when sent back' is the wordplay.
'part of' indicates the answer is hidden within the clue.
'sent back' says the letters should be written backwards.
'stimo' is hidden within 'testimony when'.
'stimo' written backwards gives 'OMITS'.
(Other definitions for omits that I've seen before include "skips" , "Leaves out or neglects" , "Forgets" , "misses out" , "overlooks" .)