Anti-theft on after replacing ignition lock

The passlock system in your car reads a code from the sensor and pellet on the ignition lock cylinder. Changing the cylinder means the new part isn't recognized. There are three ways to repair it. One that works every time is to use a higher level scan tool to reprogram the system to recognize the new cylinder. The next would be to take the old cylinder to a locksmith and have new keys cut for it and reinstall it.
The 10 minute process can take longer. It should start out with you turning the key to run, the light should start to flash and then turn on solid if it recognizes the cylinder. Once it turns on solid, turn the key to start. If successful at this point turn the key to start the engine. If the engine starts and runs it worked. If it doesn't then using a scan tool to diagnose the system to see what is and isn't working may be needed.

If you try to do the reset but the light doesn't start flashing with the new key and then turn solid the replacement key has an issue or the sensor isn't reading that the key was turned.
What vehicle is it?

Okay, that has the newer version of pass lock in it and requires a scan tool to make new keys work as there is a specific process you need to register the keys. Most auto locksmiths or the dealer can handle it. They switched to this system in 1998. It will have a chip in the key that the system reads but unless you have two known good keys you cannot program anything without the scan tool.