The authority might control electricity (5)
I believe the answer is:
power
This clue is a quadruple definition!!
'the authority' is the first definition.
(I've seen this before)
'might' is the second definition.
(being mighty)
'control' is the third definition.
(I've seen this before)
'electricity' is the fourth definition.
(I know that electricity can be written as power)
(Other definitions for power that I've seen before include "military force" , "Force, controlling influence 95)" , "Government" , "Rate of doing work" , "Political authority" .)