Tyrant not quite accepting challenge over reckless criminal (9)
I believe the answer is:
desperado
'reckless criminal' is the definition.
(I've seen this before)
'tyrant not quite accepting challenge over' is the wordplay.
'tyrant' becomes 'despot' ('despot' can be a synonym of 'tyrant').
'not quite' means to remove the last letter.
'accepting' indicates putting letters inside.
'challenge' becomes 'dare' (daring is a kind of challenging**).
'over' says the letters should be written backwards.
'dare' written backwards gives 'erad'.
'despot' with its final letter removed is 'despo'.
'despo' placed around 'erad' is 'DESPERADO'.
(Other definitions for desperado that I've seen before include "Bravo" , "Reckless outlaw" , "reckless type" , "Gangster" , "Reckless guy" .)