State goes out with a dictator (6)
I believe the answer is:
caesar
'dictator' is the definition.
(I've seen this before)
'state goes out with a' is the wordplay.
I cannot really understand how this works, but
'state' could be 'ca' and 'ca' is found in the answer.
'a' is present in the answer.
This explanation may well be incorrect...
(Other definitions for caesar that I've seen before include "Taking little bites" , "Augustus or Hadrian, say" , "Old Roman leader" , "A scare for Roman emperor" , "Roman chief like Julius" .)