Both Uses of

republic
in
Hunger Games Book #3 (Mockingjay)

We're going to form a republic where the people of each district and the Capitol can elect their own representatives to be their voice in a centralized government.
Chpt 6 *

republic = a system of government in which a majority of citizens elect representatives to make laws

But this republic idea sounds like an improvement over our current government.
Chpt 6

Definitions:

(1) (republic as in: the country is a republic)
of a system of government in which a majority of citizens elect representatives to make laws; or someone in favor of such a form of government
(2) (meaning too common or rare to warrant focus)
meaning too common or too rare to warrant focus:

As a proper noun, the word form Republican is commonly used to describe one of the major U.S. political parties. It is and has been used by many other organizations such as The Irish Republican Army.