"To have a primary" means to participate in a preliminary election where members of a political party choose their candidate for an upcoming general election. Full definition
A divorce court typically names one parent as the custodial parent who has primary responsibility for raising the child. (info.legalzoom.com)
A father who does not have primary custody of his child should never be relegated to the position or being a mere visitor in the life or his child or children. (nycfamilycourtlawyers.com)
Choose a position that does not have primary responsibilities dealing with money, private information or other people's property. (badcredit.org)