If you achieve complete remission after 6 28-day cycles of rituximab and zanubrutinib, you will be randomized to arm A, and continue to receive zanubritinib indefinitely, or arm B, and only receive zanubritinib once your mantle cell lymphoma progresses. During the study, you will record when you take zanubritinib in a drug diary. You will receive the same scans and bloodwork as the standard of care treatment for mantle cell lymphoma. You will be asked if you want to participate in optional studies. Some of these studies are questionnaires looking at the social determinants of health and your quality of life before, during and after treatment. Some will be looking at donating blood and tissue for future research studies. After treatment, you will be expected to attend follow-up appointments every 6 months.