Official comment
We don't show leads in the Partner Center, but you can provide your Partners with a list of leads they generated throughout the week.
First, create a global Rule that triggers when the First or Last Referrer field is updated depending on how your program is set up. This Rule will add the Contact to a filtering sequence.

Create the Step Sequence with multiple Rule steps, one for each Partner. In each Rule Step, check for the First or Last Referrer field to be equal to the Partner's name, and assign the contact to a Fulfillment List for that Partner.

Each Partner has a Fulfillment List. Here's an example Fulfillment List for one partner:

When you add a new Partner, you just have to add a Rule Step to the Step Sequence and create the Fulfillment List for them. From then on, they will get an email with all of their leads per the Fulfillment List settings.