Oral Islatravir (MK-8591) Once-Monthly as Preexposure Prophylaxis (PrEP) in Men and Transgender Women Who Are at High Risk for HIV-1 Infection (MK-8591-024)

Inclusion Criteria: * Has confirmed Human Immunodeficiency Virus (HIV) uninfected based on negative HIV-1/HIV-2 test result before randomization * Is sexually active with male or transgender women (TGW) partners defined as having anal sexual intercourse with a man or TGW at least once in the past month * Is at high risk for sexually acquiring HIV-1 infection based on self-report of at least 1 of the following: a) Condomless receptive anal intercourse in the 6 months prior to screening occurring outside a mutually monogamous HIV seronegative concordant relationship b) More than 5 partners (anal intercourse) in the 6 months prior to screening c) Any unprescribed stimulant drug use in the 6 months prior to screening d) Rectal or urethral gonorrhea or chlamydia or incident syphilis in the 6 months prior to screening * Participants 16 or 17 years of age must weigh ≥35 kg. Enrollment for 16- to 17-year-old participants will begin only after completion of the Sentinel Cohort IA and review of IA results by the external data monitoring committee (eDMC) * Has no plans to relocate or travel away from the site for ≥4 consecutive weeks during study participation Exclusion Criteria: * Has hypersensitivity or other contraindication to any component of the study interventions as determined by the investigator * Has chronic HBV infection or past HBV infection which could indicate risk for Hepatitis B reactivation * Has known current or chronic history of liver disease or known hepatic or biliary abnormalities, unless the participant has stable liver function tests and no evidence of hepatic synthetic dysfunction * Has a history of malignancy within 5 years of screening except for adequately treated basal cell or squamous cell skin cancer or in situ anal cancers * Has a history or current evidence of any condition, therapy, laboratory abnormality or other circumstance that might, in the opinion of the investigator, confound the results of the study or interfere with the participant's participation for the full duration of the study, such that it is not in the best interest of the participant to enroll * Has taken cabotegravir, lenacapavir, or any other long-acting HIV prevention product at any time * Is currently receiving or is anticipated to require any prohibited therapies outlined in the study from 30 days prior to Day 1 through the duration of the study * Is currently participating in or has participated in an interventional or prevention clinical study with an investigational compound or device, within 30 days prior to Day 1 through the duration of the study * Has exclusionary laboratory values within 45 days prior to Day 1