RecoverPC: A Phase 2 Study of RElugolix Versus GnRH Agonist Quality of Life (QOL) and Testosterone reCOVERy in Men With Prostate Cancer

Inclusion Criteria: * Participants must have a histologic diagnosis of prostate adenocarcinoma. * Participants must be eligible for treatment with 6 months of ADT with leuprolide depot or relugolix without additional systemic therapies other than first generation androgen receptor antagonists (eg. bicalutamide, nilutamide, flutamide). * Participants cannot have received prior GnRH agonist or antagonist therapy. * Patients must have testosterone level \> 200 ng/mL prior to initiation of ADT. * Age ≥18 years. * ECOG performance status ≤2 (Karnofsky ≥60%, see Appendix A). * Life expectancy of greater than 12 months * Participants must have adequate organ and marrow function as defined below: * leukocytes ≥3,000/mcL * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * total bilirubin ≤ institutional upper limit of normal (ULN) unless known or suspected Gilbert syndrome * AST(SGOT)/ALT(SGPT) ≤3 × institutional ULN * creatinine ≤ institutional ULN OR * glomerular filtration rate (GFR) ≥50 mL/min/1.73 m2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m2 (see Appendix B). * Human immunodeficiency virus (HIV)-infected participants on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. * For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants should be class 2B or better. * The effects of relugolix and leuprolide on the developing human fetus are unknown. For this reason and because GnRH agents are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of relugolix or leuprolide depot administration. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * History of major adverse cardiac event, including myocardial infarction, new congestive heart failure (CHF) or CHF exacerbation, or stroke, within the past 6 months. * Participants who have prior or planned concurrent treatment with second generation AR targeted therapies (such as abiraterone, enzalutamide, darolutamide, apalutamide). * Participants who are receiving any other investigational agents. * Patients with brain metastases will be excluded from the study as intermittent hormonal therapy is not standard of care treatment for this population. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to leuprolide depot or relugolix. * Participants with uncontrolled intercurrent illness. * Participant is unable to swallow pills.