In Revenge of the Sith, when Mace Windu, Kit Fisto, Agen Kolar and Saesee Tin arrest Palpatine in his office. The script is as follows:
Mace Windu: In the name of the Galactic Senate of the Republic, you're under arrest, Chancellor.
Supreme Chancellor: Are you threatening me, Master Jedi?
Mace Windu: The senate will decide your fate.
Supreme Chancellor: I AM the senate!
Mace Windu: NOT YET.
Since Palpatine is the Chancellor of the Republic, and retorted by Mace Windu that he is not the Senate. Does that mean that a Senate is more of a higher authority than the Chancellor? Palpatine can order the Clones in any matter.The Chancellor is the just like the President of a country. In this sense, Palpatine is the president of the republic. In real life terms, A President has higher authority than a Senator.