Yes in most cases you can trade in your car for another car when you're financing it.
Some car dealerships will allow you to trade in your car even when you're still financing it and paying on it and then the car dealership or finance company will pay off the car you're trading in and then the car dealership will take ownership of the car.
I have done this before when I wanted to get into a new car and I was financing another car and still owed on it.
The car dealership paid off the car and took it as a trade in and then got me financed with the new car so I was able to trade in the financed car and get financing on a new car.
So yes it's possible to trade in your car or other vehicle even when you're still financing the car but you have to get the dealership to pay the car off to the other finance company.