Move bacteria from old tank
You can help the cycle by moving bacteria from the filter of the established tank. Take some filter media or some gravel from that old tank and move it to the filter of the new tank.
If you have a canister filter, clean it out and take all the dirty water from rinsing the filter media and put it into the new filter or pour it into the new tank. Most of that "dirt" is the bacteria you need.
If it is a hang-on-back type of filter, you can take the cartridge or pad out and rinse it in the new tank.
The bacteria you want are also on the gravel of the old tank, especially if that tank had an undergravel filter. In that case, take some of the top gravel, a handfull, and put it into the filter (in a mesh bag or a stocking so you can take it out after a few weeks)
The bacteria are also on the decorations of the old tank, so if you can move a plant, real or fake, to the new tank, that will help.