I think I have the code working the way I'd like it to. Onto the TestClass which of course is giving me some issues.

Here's the trigger

trigger syncSuppression on Opportunity (after update) {
    List<suppression__c> suppressionList = new List<suppression__c>();
    //We'll contain the list of Ids that we need to manage, since not every opportunity necessarily needs to be processed this
    //may be different than what's in the trigger.new value
    Set<Id> opportunitiesToProcess = new Set<Id>{};
    for (Opportunity o:trigger.new) {        
        //Check if the latest opportunity's stage name is 'Submitted' since this is the only one that needs to be pushed into the suppression object
        //Since we only want to do this on the "first" time it's become submitted we'll check first
        //1) If Trigger.isInsert is true, then the trigger is currently firing due to an "insert" operation of an opportunity
        //2) If it's not an insert, then we are getting the OLD record from the oldMap. The oldMap is populated during update operations
        //     and will contain the value of the records before the update occurred
        //     So we'll check the old and see if the stage name is not submitted, if it wasn't we can assume since the new one is submitted it's being changed
       if (o.StageName == 'Submitted'  && 
           (Trigger.isInsert || Trigger.oldMap.get(o.Id).StageName != 'Submitted'))
        {
            opportunitiesToProcess.add(o.Id);
        }        
    }
    
    //If there are no opportunities that match the criteria above we might as well break out and not do any more processing
    //! is the NOT operation for the value, so basically it's saying if the lits of opportunities to process is not empty
    //You can also read it like this:
    //opportunitiesToProcess.isEmpty() == false
    if (!opportunitiesToProcess.isEmpty())
    {
        //Here is where you can get the information for the primary campaign's client account
        for (Opportunity o : [ select Id, ClientID__c, Campaign.Client_Account__r.id, Account.Name, Account.Website, Main_Contact__r.Email_Domain__c from Opportunity where Id IN :opportunitiesToProcess ])
        {
            //Do stuff here
            suppression__C newSuppression = new suppression__c();
            newSuppression.Client__c=o.Campaign.Client_Account__r.id;
            newSuppression.Company_Name__c=o.Account.Name;
            newSuppression.website__c=o.Account.Website;
            newSuppression.email_domain__c=o.Main_Contact__r.Email_Domain__c;
            suppressionList.add(newSuppression);        
        }
                
        insert suppressionList;        
    }
}

 And Here's the TestClass. I'm getting a "

System.DmlException: Update failed. First exception on row 0 with id 006Q000000BVhGAIA1; first error: CANNOT_INSERT_UPDATE_ACTIVATE_ENTITY, syncSuppression: execution of AfterUpdate

caused by: System.DmlException: Insert failed. First exception on row 0; first error: REQUIRED_FIELD_MISSING, Required fields are missing: [Client__c]: [Client__c]

Trigger.syncSuppression: line 38, column 1: []"

So what I'm trying  to do is create a new opportunity with one stagename and then update the opportunity stagename to Submitted to fire the trigger. It says the code has 100% coverage, but then i get an error on the Tests column of developer console.

@isTest

private class syncSuppressionTest {

static testMethod void validateSyncSuppression(){
// new opportunity
Opportunity o = new Opportunity(
Name='testsync', 
StageName='0 BANT',
Type='New Client QSO Opportunity',
CloseDate= date.today(),
CampaignID='701Q0000000Ofq8',
Main_Contact__c= '003Q000000hv2yI'
);
System.debug('new op made: ' + o.name);

//insert op
insert o;

//update op
o.StageName='Submitted';
update o;
System.debug('new op updated: ' + o.StageName);
    
}

}