This phase II trial evaluates the best duration for relugolix to be given in combination with radiation therapy when treating patients with high risk prostate cancer. Prostate cancer is a hormonal influenced cancer. Part of the usual treatment for patients with prostate cancer is androgen deprivation therapy (ADT). ADT is used to lower the amount of testosterone in the body, because testosterone appears to help prostate cancer grow. Relugolix works to reduce testosterone levels, which may inhibit proliferation of prostate cancer cells. It is approved by the Food and Drug Administration to treat prostate cancer. Adding relugolix to standard radiation therapy might work better and have fewer side effects than prior forms of hormonal therapy, but the optimal duration of relugolix in combination with radiation is not known.

PRIMARY OBJECTIVE:

I. To compare the biochemical recurrence rate between 12 and 24 months of relugolix in patients with high risk prostate cancer treated with combination external beam radiation and brachytherapy.

SECONDARY OBJECTIVES:

I. To compare the composite quality of life in patient treated with 12 months and 24 months of relugolix as assessed by the Expanded Prostate Composite Index Short Form (EPIC-26) instrument.

II. To compare the treatment related toxicity between 12 months and 24 months of relugolix as assessed by Common Terminology Criteria for Adverse Events version 5.0. (CTCAE v 5.0) criteria.

III. To compare the rate of major adverse cardiovascular events (MACE) in patients treated with 12 and 24 months of relugolix.

IV. To establish the rate of patient compliance using patient reported drug diary.

V. To compare the rate of testosterone recovery after 12 and 24 months of relugolix.

EXPLORATORY OBJECTIVE:

I. To establish Decipher genomic classifier as predictor of cancer control.

OUTLINE: Patients are randomized to 1 of 2 arms.

ARM A: Patients receive relugolix orally (PO) once daily (QD). Cycles repeat every 3 months for 12 months in the absence of disease progression or unacceptable toxicity. Beginning 30 to 180 days after start of relugolix, patients undergo brachytherapy and external beam radiation over 25 fractions. Patients undergo bone scan, computed tomography (CT) or magnetic resonance imaging (MRI) or prostate-specific membrane antigen (PSMA) positron emission tomography (PET) scan during screening. Patients also undergo dual x-ray absorptiometry (DEXA) scan and may optionally undergo blood sample collection throughout the trial.

ARM B: Patients receive relugolix PO QD. Cycles repeat every 3 months for 24 months in the absence of disease progression or unacceptable toxicity. Beginning 30 to 180 days after start of relugolix, patients undergo brachytherapy and external beam radiation over 25 fractions. Patients undergo bone scan, CT or MRI or PSMA PET scan during screening. Patients also undergo DEXA scan and may optionally undergo blood sample collection throughout the trial.

After completion of study treatment, patients in Arm A are followed up every 3 months for 12 months and then every 6 months for up to 36 months and patients in Arm B are followed up every 6 months for up 36 months.

Inclusion Criteria:

• Ability of participant or Legally Authorized Representative (LAR) to understand this study, and participant or LAR willingness to sign a written informed consent

• Age ≥ 18 years

• Eastern Cooperative Oncology Group (ECOG) performance status 0 - 1

• Life expectancy > 5 years

• Patient diagnosed with National Comprehensive Cancer Network (NCCN) high risk and very high risk prostate cancer.

  • High risk is defined as:

    • T3a or
    • Grade group 4 or 5 or
    • Prostate-specific antigen (PSA) > 20 ng/mL

  • Very high risk is defined as:

    • T3b to T4 or
    • Primary Gleason pattern 5 or
    • Two or three high-risk features or
    • > 4 cores with grade group 4 or 5

• Eligible for treatment with combination brachytherapy, external beam radiation, and ADT

• Leukocytes >= 1.0 K/UL

• Platelets >= 100 K/UL

• Hemoglobin ≥ 9 g/dL

• Aspartate aminotransferase and alanine aminotransferase ≤ 2.5 x upper limit of normal (ULN)

• Men with partners of child-bearing potential must agree to practice sexual abstinence or to use the forms of contraception listed for the duration of study participation and for 2 weeks following completion of relugolix therapy

Exclusion Criteria:

• Simultaneously enrolled in any therapeutic clinical trial
• Current or anticipating use of other anti-neoplastic or investigational agents while participating in this study
• Diagnosed with a psychiatric illness or is in a social situation that would limit compliance with study requirements
• Has a known allergic reaction to any excipient or component contained in the study drug formulation
• Active grade 3 (per the National Cancer Institute [NCI] CTCAE, version 5.0) or higher viral, bacterial, or fungal infection within 2 weeks prior to the first dose of study treatment
• Current androgen deprivation therapy (unless testosterone > 50 ng/dL). Please note prior or concurrent bicalutamide at 50 mg/daily or less is allowed. Prior androgen deprivation therapy is allowed if testosterone has recovered to > 50 ng/dL
• Prolonged echocardiogram corrected QT (QTc) interval > 440 ns
• Prior pelvic therapy that would significantly overlap with radiation treatment fields
• Prior prostatectomy