This phase IV trial studies the effects of testosterone replacement therapy (TRT) on treatment outcomes in hypogonadal men with prostate cancer that has not spread to other parts of the body (localized) and who are on active surveillance (AS). AS in prostate cancer involves closely watching the patient's condition through regular physical exams and blood tests, but not giving treatment unless there are changes in test results. It can be a practical alternative to treatment in localized prostate cancer. Hypogonadal men have low testosterone associated with symptoms such as low libido and erectile problems. TRT can be used to treat hypogonadism by increasing testosterone levels, which may improve associated symptoms. TRT is often not used in men with prostate cancer due to concerns it may lead to the cancer growing or spreading. This may lead hypogonadal men to have a poor quality of life or to discontinue AS. TRT may improve treatment and quality of life outcomes in hypogonadal men with localized prostate cancer on active surveillance.