Keep quiet about a Persian ruler (4)
I believe the answer is:
shah
'persian ruler' is the definition.
(I've seen this before)
'keep quiet about a' is the wordplay.
'keep quiet' becomes 'shh'.
'about' is an insertion indicator.
'shh' placed around 'a' is 'SHAH'.
(Other definitions for shah that I've seen before include "Former ruler of Iran" , "Former Persian title" , "Sovereign ousted in 1979" , "Title of Iranian monarch" , "Persian king" .)