The current thinking is that if you are post treatment with curative intent, have low stable PSA, no evidence of disease, and your Testosterone is lower than the normal range, there's no reason not to go on to TRT. This needs to come with a talk on theoretical risks and more frequent PSA (and Testosterone) monitoring.
You need to get past your GP (who I would not expect to know this) and referred to Andrology (or Urology if your hospital doesn't have a separate Andrology department).
We could keep everyone who's had curative treatment on lifelong HT and it might even reduce recurrence, but this is counterproductive because it has significant risks in itself, so we don't do this. You being refused TRT after finishing HT is indeed effectively being kept on lifelong HT, which as I said we don't do for good reasons.
However, it's not just a case of taking Testosterone in some way. You need the PSA and Testosterone level monitoring with it. It's not easy to administer Testosterone and get the level in the body correct range, and there's likely to be some trial and error with dosing at least to start with.