If a Contact is marked as Is_Primary__c = true, automatically uncheck Is_Primary__c on all other sibling Contacts under the same Account.

trigger ContactTrigger on Contact (after insert, after update) {
    if (ContactHandler.running) return;
    Map<Id, Id> primaryByAcc = new Map<Id, Id>();
    for (Contact c : Trigger.new) if (c.Is_Primary__c && c.AccountId != null) primaryByAcc.put(c.AccountId, c.Id);
    if (primaryByAcc.isEmpty()) return;
    List<Contact> sibs = [SELECT Id, AccountId FROM Contact WHERE AccountId IN :primaryByAcc.keySet()
                          AND Is_Primary__c = true AND Id NOT IN :Trigger.new];
    for (Contact s : sibs) s.Is_Primary__c = false;
    ContactHandler.running = true;
    update sibs;
    ContactHandler.running = false;
}