The clergy weren't explicitly backing the Shah, they were just fearful of anything like communism happening, since most communist countries/communists are aesthetes.
Iranian clergy as an institution starting coming into political power, really, around the time of the Russian-Persian wars, were one of the highest ranking Shia scholars in Iran issues a fatwa supporting the war against Russia.
The clergy weren't explicitly backing the Shah, they were just fearful of anything like communism happening, since most communist countries/communists are aesthetes.
Iranian clergy as an institution starting coming into political power, really, around the time of the Russian-Persian wars, were one of the highest ranking Shia scholars in Iran issues a fatwa supporting the war against Russia.