Slip over in despair or regret (5)
I believe the answer is:
error
'slip' is the definition.
(slip can mean an error or mistake)
'over in despair or regret' is the wordplay.
'over' says the letters should be written backwards.
'in' says the answer is hidden in the clue.
'rorre' is hidden within 'despair or regret'.
'rorre' backwards is 'ERROR'.
(Other definitions for error that I've seen before include "Mistake from terrorist" , "heresy" , "Faux pas" , "Gaffe" , "1 down" .)