For any newbs here, HCG is injected subcutaneously in a fold of skin in your abs or love handle region typically. Do not inject in your private parts. HCG, as I understand it, mimics LH (leutenizing hormone), which is the natural signal to your testicles to generate testosterone by your own natural production methods.
So, during TRT, by definition, your body is shut down, meaning the test provided by your weekly injections is enough that your body never needs to signal for its own natural production to kick in. That causes the testicles to atrophy (i.e., shrink). Most of us guys don't care about that, but I do think there is some advantage to keeping your natural production going (even if it's not working optimally, hence the TRT).
I believe Dr. Crisler's protocol that was pretty popular for TRT was you pin your long estered test (e.g., test Cyp) once per week, for example, on Sunday. 5 days after pinning, that test level in your bloodstream is beginning to decline, so on day 5 and day 6 (the next Friday and the next Saturday), you would pin HCG (250IUs) on each of those days. That would keep your natural production going, and boost your test levels slightly so that if you looked at your test levels throughout the week, they stayed a bit more level than otherwise.
I've been on test for the last 15 years, and I still take the HCG.