My effort to get a TUE some years back ended with a brick wall.
I was on a med for a short time that had, if you used one particular variety, a very small amount of a banned substance (it was listed as a blocker, something that blocked labs from detecting naughty stuff like testo, but in amounts that would not do that particular job anyway).
I only applied for the TUE in case I was tested out of comp, and in case I ever had to use the variety that had the blocker (sometimes there is a chance that the pharmacist would be out of my brand/variety so would provide the "bad" stuff) even though I would be on it for only a few months with ZERO performance enhancement and I was not intending to use the other brand.
Anyhoo, sent off all the paperwork to ASADA. A few weeks later I get a letter telling me that the application was rejected because I needed a specialists approval, not my local GP. Apparently, a doctor isn't a doctor, even though their instructions never mentioned the requirement for a specialist, just a form to be filled out "by your doctor". Who'd a known, right?
So, to get a specialist approval for something I was not using would require another GP appointment ($ + time) to get a recommendation to see a specialist (kidney) which would take some months (plus lots more $$ and time) to get past the wait list by which time I would no longer be using the prescription meds that didn't have anything in them that was banned (unless, as stated, I had to use another type due to supply issues).
So I gave up.
Also, in the process I found that if you DID get a TUE for anything, it had to also get passed by the fed (for me at that time it was the IPF affiliated PA), so getting a TUE from ASADA was just the first step.
Also, from memory, the IPF (and affiliates) will not accept a TUE for testosterone treatment. So you might get an ASADA or WADA TUE but still not allowed to compete. Unless you are from Russia because in the IPF Russian lifters don't get tested unless you are at the world champs and get on the podium and forget to make your annual "subscription" payment.
*cough*
Not sure what the status is right now with transgender lifters but I'm certain that the only trans competing would be men competing as women so I assume that testo suppression would be used. But as I said, not sure of that particular status.
So, to summerise, you won't get to compete with a TUE for testosterone. And if you do (cos you didn't tell anyone) you will get pinged if you are tested cos it's not the amount of testo you are using (well, it can be if you go overboard and are taking 3gm per week like Oni) but the ratio of test to epitestosterone, which will get thrown out of whack by even small doses.
This is why it's pretty plain to see when someone who is a masters lifter is "on the juice" when their numbers increase or stay level as they get older. That's not how the human body works.