Shower reportedly govern (5)
I believe the answer is:
reign
'govern' is the definition.
(reigning is a kind of governing)
'shower reportedly' is the wordplay.
'shower' becomes 'rain' ('rain shower' can be a synonym of 'shower').
'reportedly' indicates a 'sounds like' (homophone) clue.
'rain' is a homophone of 'REIGN'.
(Other definitions for reign that I've seen before include "Sovereignty" , "Period during which someone is dominant" , "Period of monarch" , "Rule of monarch" , "Spell in office" .)