You state:
What I have is a mouse click and when you click on to a grid (2D array), the player X and Y pos should go to that position.
This doesn't sound like it needs a "Game Loop" at all. What you need for this behavior is simply a MouseListener, and that's it.
Also and to reiterate my comment, I fear that the advice you received in your other recent question was not good advice, since they advised you to use a java.util.Timer
with a Swing application, and that can be dangerous. Usually it's better to use a javax.swing.Timer
also known as a "Swing Timer".
For better advice, you will want to give more details of just what you're trying to create.
Edit
You state:
I want to refresh my Jpanel and make it look like as if the square is moving to that position.
So do that -- in a MouseListener.