Deity with insufficient authority! (4)
I believe the answer is:
thor
'deity' is the definition.
(Thor is an example)
'with insufficient authority' is the wordplay.
'with' indicates a hidden word.
'THOR' is hidden in the letters of 'insufficient authority'.
(Other definitions for thor that I've seen before include "Wielder of hammer" , "can be classed as immortal" , "Norse god of thunder - a weekday is named after him" , "Thursday is named after this Scandinavian god" , "Comic superhero" .)