A tyrant is the chap to shoot (6)
I believe the answer is:
despot
'a tyrant' is the definition.
('despot' can be a synonym of 'tyrant')
'the chap to shoot' is the wordplay.
'the chap' becomes 'des' (**).
'to shoot' becomes 'pot' (I've seen this in other clues).
'des'+'pot'='DESPOT'
'is' acts as a link.
(Other definitions for despot that I've seen before include "Cruel absolute ruler" , "Tyrant, oppressor" , "Caesar for one" , "Posted (anag)" , "Arbitrary ruler" .)