How to use QtPainter after starting the UI and later when a button is pressed?

To draw directly onto a widget you can override it's paintEvent. The thing to remember when doing so is that paintEvent fires every time the Widget deems it necessary to redraw itself e.g. when it has been resized or moved. This means that when implementing your own version of paintEvent you need to draw all the shapes you want drawn on your widget. Note that paintEvent is rarely called directly. If you want the widget to redraw itself, you should call update() which will schedule a paintEvent for you.

Here is a simple example where arbitrary rectangles are added to a canvas when clicking on a button. The rectangles are stored in an array in the Canvas object. In Canvas.paintEvent, we create an instance of QPainter and use this object to draw all the rectangles in the array.

from PyQt5 import QtWidgets, QtGui, QtCore
from random import randrange

class Canvas(QtWidgets.QWidget):
    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.rectangles = []

    def add_rectangle(self, rect, color):
        self.rectangles.append((rect, color))
        self.update()

    def paintEvent(self, event):
        painter = QtGui.QPainter(self)
        brush = QtGui.QBrush(QtCore.Qt.white)
        painter.setBrush(brush)
        painter.drawRect(event.rect())

        pen = QtGui.QPen()
        pen.setWidth(3)
        for rect, color in self.rectangles:
            pen.setColor(color)
            painter.setPen(pen)
            brush.setColor(color)
            painter.setBrush(brush)
            painter.drawRect(rect)

class MyWindow(QtWidgets.QWidget):
    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.canvas = Canvas(self)
        self.button = QtWidgets.QPushButton('Add rectangle')
        self.button.clicked.connect(self.add_rectangle)

        self.layout = QtWidgets.QVBoxLayout(self)
        self.layout.addWidget(self.canvas)
        self.layout.addWidget(self.button)
        self.resize(500,500)

    def add_rectangle(self):
        w = self.canvas.width()
        h = self.canvas.height()
        x0, y0 = randrange(w), randrange(h)
        x1, y1 = randrange(w), randrange(h)

        shape = QtCore.QRect(min(x0,x1), min(y0,y1), abs(x0-x1), abs(y0-y1))
        color = QtGui.QColor.fromRgb(*(randrange(256) for i in range(3)), 180)
        self.canvas.add_rectangle(shape, color)


if __name__ == "__main__":
    app = QtWidgets.QApplication([])
    window = MyWindow()
    window.show()
    app.exec()