Before you get rid of your previous computer, you must remove the license from the previous device using the Help > Revoke License command (or the Help > Deactivate ExtendSim command if prior to ExtendSim 10.0.5). If you don't do this, you won't be able to automatically activate on your new device.
If you are still using ExtendSim 9 or other retired release...
Go to Settings > Apps and uninstall ExtendSim 9 from your old device.
Use the original installer file you either downloaded from the ExtendSim Store or from your original CD to install on the new device. Then, be sure you are using the newest release as discussed in Updating ExtendSim.