Drawing a shape on a JPanel which already uses the paint method

Let’s say I have two classes, the first extends JPanel and using Graphics draws a playing board on it. The second makes a JFrame and adds the panel to it.

You can imagine the frame looking something like this:
sample JFrame

I now want to add an ellipse to a specific rectangle on click. I understand that I would be using a two-dimensional array in order to get the position I wanted, but I don’t understand how the ellipse itself would be drawn on to the existing panel since I used the paint(Graphics g) to draw the playing board.

Here is the code for drawing the board itself if you need it:

class MyBoard extends JPanel {
    private static int height = 6;
    private static int width = 7;
    private static int squareSize = 100;
    private int board[][] = new int[height][width];

    public void paint(Graphics g) {
        for (int i = 0; i < height; i++) {
            for (int j = 0; j < width; j++) {
                g.drawRect(j * squareSize, i * squareSize, squareSize, squareSize);