This phase II trial studies how well nivolumab and brentuximab vedotin work in treating older patients with untreated Hodgkin lymphoma. Monoclonal antibodies, such as nivolumab, may block cancer growth in different ways by targeting certain cells. Biological therapies, such as brentuximab vedotin, use substances made from living organisms that may stimulate or suppress the immune system in different ways and stop cancer cells from growing. Nivolumab and brentuximab vedotin may work better in treating older patients with untreated Hodgkin lymphoma.