I want to power my motor shield without my UNO. I have connected the
-ve terminals resulting in lighting up of the LED.
Is there any way to control the motors in this arrangement from the Arduino?
I'm not sure I understand what you are asking because what you are trying to do doesn't make much sense.
The motors connected to the motor shield are controlled by the output pins of the Arduino that the motor shield is plugged in to.
You could run jumper leads from an separate Arduino into your unplugged motor shield, but that's just extending what you already have. You really do need some form of controller, not necessary a microprocessor, otherwise how can you go forwards and backwards?
Is the problem you have put the Arduino into a plastic case and you can't plug the motor shield in any more? If so get a set of long male to female connectors (they look like the Arduino connectors) and use them as extensions.
Is the problem you have a different format of board and can't plug it in? If so use the wires method to form the correct connections.
I hope that answers your question, if not please try and explain what I'm misunderstanding.