A form of government in which the leader is not a monarch and certian citizens have the right to vote

Answer: A republic

Further detail:

A republic differs from a democracy in that when a government is fully a democracy, that means voting and participation in government by all citizens. A republic may limit voting and political rights to certain types of citizens. Many republics in history, for instance, have limited voting rights to those who owned a certain amount of property. Britain was like that for a long time, and the United States started out that way as well.

We think of the United States today as a democratic republic, because voting rights are granted to all citizens age 18 or older, but voters elect representatives who serve in the government of the republic on their behalf.