trigger contactPicklist on Contact(before insert){
    Map<ID,Contact> accountIds = new Map<ID,Contact>();
    for(Contact c : Trigger.New){
        accountIds.add(c.AccountId,c);
    }    
    for(Account acc : [Select Id, (Select Id, somecustomPicklistField from Contact) From Account Where Id IN accountIds.keyset()]){
        for(Contact con : acc.contacts){
            //Checking the picklist value, what user has selected
            if(accountIds.get(acc.Id).somecustomPicklistField == 'Primary'){
                //Checking the contacts already exists in the database
                //You can customize the below if and else conditions based on your requirements.
                if(con.somecustomPicklistField == 'Primary'){
                    con.addError('There is already one primary contact exists.');
                }
                else{
                    
                }
            }
            //Checking the picklist value what user has selected.
            else if(accountIds.get(acc.Id).somecustomPicklistField == 'Secondary'){
                //Checking the contacts already exists in the database.
                //You can customize the below if and else conditions based on your requirements.
                if(con.somecustomPicklistField != 'Primary'){
                    con.addError('There is no Primary Contact for this current');
                } 
                else{
                    
                }
            }
        }
    }
}