elect a person
In a political primary, you have to register by political party.
Primary Party (NovaNet) Primary (Apex)
Voting in a CLOSED primary (apex)
A political party's closed primary election is a primary election that is open only to members of the party.
Primary
Democratic Party.
By caucus of members of a political party, by state party conventions, or by primary elections, or by all of the above in some states.
Democrats.
voter in a closed primary
The sounds like a primary election.
an organization with the primary purpose of running candidates for political office and coordinating the actions of officials elected under the party banner
These are known as primary elections or primaries.