Starter operating in run position

We need to start with checking the voltage at the starter to find out if the relay is sticking or the starter solenoid is shorted.

Since you just replaced the starter and it was not doing this before, I suspect the starter is the issue so I would return it and swap it out.

However, here is a guide that will help with checking voltage at the starter:

https://www.2carpros.com/articles/how-to-check-wiring

https://www.2carpros.com/articles/how-to-replace-a-starter-motor

I am attaching the wiring diagram below which will help with this as well.

Please let me know what questions you have.

Thanks