Rat cannily becomes despotic (10)
I believe the answer is:
tyrannical
'despotic' is the definition.
(I know that despotic can be written as tyrannical)
'rat cannily becomes' is the wordplay.
'becomes' is an anagram indicator.
'rat'+'cannily'='ratcannily'
'ratcannily' is an anagram of 'TYRANNICAL'.
(Other definitions for tyrannical that I've seen before include "Autocratic" , "Unjustly oppressive" .)