Trigger:
trigger DealerPrimaryContact on Contact ( after insert, after update) {
Set<Id> DealerAccIdSet=new Set<Id>();

   for(Contact cont:Trigger.new)
   {
     if(cont.AccountId !=null && cont.Primary__c == True )
     {

        DealerAccIdSet.add(cont.AccountId); 
     }
   }

   if(!DealerAccIdSet.isEmpty()){

      List<Account> DealerAccListToUpdate=new List<Account>();

        for(Account acc: [SELECT id,(SELECT id,email FROM Contacts where Primary__c = True ) FROM Account WHERE Partner_Type__c = 'Dealer' And Id IN :DealerAccIdSet] ){

         acc.Primary_Contact_Email_Address__c=acc.Contacts[0].email;

          DealerAccListToUpdate.add(acc);

       }

       if(!DealerAccListToUpdate.isEmpty()){

         try{

            Update DealerAccListToUpdate;

         }Catch(DmlException de ){

           System.debug(de);

         }

       }

   }
}

Test Class:
@isTest (SeeAllData = false)
public class TestDealerPrimaryContact {
    @isTest    
    public static void DealerPrimaryTestClass() 
    {
 
        Account a = new Account();
            a.Name= 'Test Dealer Account';
            a.Type= 'Dealer / Distributor';
            a.Partner_Type__c = 'Dealer';
            a.Tier__c = 'Stocking Dealer';
            a.Status__c = 'Active';     
            a.RecordTypeId = '012j0000000cfvw';
            a.Primary_Contact_Email_Address__c ='';
            insert a;
    
       Contact con = new Contact();
            con.Contact_Types__c= 'Employee';
            con.FirstName= 'Tester';
            con.LastName= 'testy';
            con.Email='test@gmail.com';
            con.Primary__c = false;
            con.Phone = '111-111-2222';  
           con.Primary__c=true;
         
               
        test.startTest(); 
        
       //   insert a;
          insert con;
          con.AccountId= a.Id;
          a.Primary_Contact_Email_Address__c =con.Email  ;
          update con;
          update a;
        test.stopTest();        
       
    }

}