On the rocks in your old tank, since you have a UGF(under gravel filter), live thousands upon thousands of beneficial bacteria called Autotrophics. These bacteria live off of ammonia. When ammonia is present in a tank (ammonia comes from fish waste, rotting fish food/other debris, but mainly from respiration; when a fish breathes, the fish gives off ammonia). Ammonia is toxic to all fish if over a level of .25 ppm (which is very little). These beneficial bacteria will process/eat the ammonia in the tank, so that the ammonia level is at a constant 0 ppm (safe for fish). When these bacteria eat ammonia, ammonia then turns into nitrite. Nitrite is also toxic to fish if over .25 ppm. So again, there is another type of Autotrophic bacteria that process/eat Nitrite. When Nitrite is processed, it turns into Nitrate. Nitrate is not as toxic to fish unless in very large amounts (400+ ppm). In your tank, I would not expect nitrate to exceed about 40 ppm. There are no bacteria that process nitrate, so weekly water changes must be performed to keep the nitrate levels down.
So, Ammonia -> Nitrite -> Nitrate -> Weekly water change.
Now, it takes time to colonize enough bacteria to constantly keep the ammonia and nitrite levels at 0 ppm.
You see... these bacteria do not create ammonia. Ammonia is present in the tank when fish are present.
So, you must add ammonia to the tank to keep the bacteria alive. A fishless cycle uses bottled ammonia to "simulate" a fish, or a harder way is a fish-in cycle where fish are added directly to the tank to produce ammonia. However a fish-in cycle leaves the fish to be present to high levels of ammonia and nitrite until the bacteria colonize enough to keep ammonia and nitrite at 0 ppm. This is why a fish-in cycle is not recommend; but one should do a fishless cycle.
So, take some rocks from your old tank, and just rinse the rocks off in your new tank and put the rocks back in your old tank. Then I would like to see you do a fishless cycle, where the bacteria you just added would kick start the fishless cycle.
But, if you do not want to do a fishless cycle, you could do a fish-in cycle, but you will be doing a lot of water changes until the fish-in cycle completes. Read this to learn about fish-in cycling:
http

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-FHM