You have to erase the old text first. Surfaces created by Font.render
are ordinary surfaces. Once a Surface
is blit, its contents become part of the destination surface, and you have to manipulate the destination surface to erase whatever was blit from the source surface.
One way to erase the destination surface is to blit a background surface onto it. The background surface is what the destination surface would look like without anything like text or sprites on it. Another way is to fill the surface with a solid color:
# pygame initialization goes here
screen = pygame.display.get_surface()
font = pygame.font.Font(None, 40)
font_surface = font.render("original", True, pygame.Color("white"));
screen.blit(surface, (0, 0))
screen.fill(pygame.Color("black")) # erases the entire screen surface
font_surface = font.render("edited", True, pygame.Color("white"));
screen.blit(surface, (0, 0))