Yes. I love the, “The US isn’t a democracy, it’s a Republic!” crowd. A Republic is a form of representatives democracy. The majority elects representatives who then vote on behalf of their constituents. They speak with such confidence but are completely wrong.
EDIT: The definition of a republic is, “a state in which supreme power is held by the people and their elected representatives, and which has an elected or nominated president rather than a monarch.” Ancient republics may have been different but we don’t live in the ancient world. Not every country that calls itself a Republic is a Republic. The DPRK and Republic of Iran, for example, are a dictatorship and a theocratic autocracy. They are not republics.
The People are the citizens of the state not the white people, or the Christian people, or the Republican people, or the people you agree with. The People are all of the people. It is only a Republic if every single citizen has the right to vote and equal access to the ballot box. If you are trying to disenfranchise people who don’t vote the way you want them to you’re not a Republican, you’re a RINO.
The People may only exercise supreme power if they freely and fairly elect their representatives. If you’re trying to limit the number of polling stations in areas where people don’t vote the way you want them to, or to stop counting of ballots before every ballot is counted, or to make it difficult to vote by mail, or early, or on Sunday you are not a Republican, you’re a RINO.
In a Republic, every citizen has the right to vote, their votes all carry the same weight, and they have equal access to the ballot box. If you don’t have those things not only are you not a democracy but you’re not a republic either.
Just a technicality: Not all republics are democracies. A republic could be an oligarchy or a theocracy. The main division is between monarchy and republic.
The definition of a Republic is, “a state in which supreme power is held by the people and their elected representatives, and which has an elected or nominated president rather than a monarch.”
If the people don’t elect their representatives and president then it’s not a Republic. The DPRK, for example, is not democratic and is therefore not a Republic. Autocracies are republics in name only.
I suppose it does depend on which definition one is using. The more academic definition puts them as contrasting with monarchies. With that, the DPRK and other autocracies world not be a republic, not due to a lack of democracy but due to a lack of representative-based government. “Representative” here meaning multiple individually who are ostensibly representing the public interest (frequently, this is someone that they fail to do).
What makes a republic democratic or not is HOW the representatives are appointed. In a theocratic republic, they could be appointed by the state church, for example.