For men who have finished treatment for prostate cancer, and which appears to have worked with no evidence of disease, if they are low on Testosterone, then treating this does not appear to increase risk of prostate cancer recurrence. There is even the suggestion from some places that low T (but not as low as hormone therapy levels) could be a contributory factor for prostate cancer.
This is a relatively new finding, the mantra for years having been, no you can't have TRT (Testosterone Replacement Therapy) if you ever had prostate cancer. However, you will certainly need your PSA regularly monitored (as well as your T).
As a former prostate cancer patient, you will probably need to be referred to an andrologist to investigate this properly, and they should ask permission of your oncologist before treating. Low T is not simply a matter of measuring T levels, because the right level varies, anything from about 8nmol/L to 26nmol/L in different people but fairly constant in any one person. I spoke with someone who is suffering with low T symptoms, and he is around 10 or 11nmol/L. While that might be within the normal range, his Luteinising Hormone and FSH levels are very high, which means his brain is trying unsuccessfully to raise his T level higher, so his normal is indeed higher than 10 or 11, whereas that level might be normal for someone else. In this case it's due to damage to testicles, and they are generating the max they can. The wide range of normal level is because different people have more or less sensitive androgen receptors. If you have more sensitive androgen receptors, your normal T level will be lower. However, there is often a gradual drop in T levels with age, and being overweight also drops your T levels because Aromatase enzyme in body fat converts T to estrogens (female sex hormones), so the more body fat you have, the more of your T gets converted to estrogens. That not only loses you some T, but estrogens suppress the generation of T in the first place, so that's a double whammy.