When you play a new Draw Rule, if the new Draw Rule is more than the old Draw rule. Take the difference between the 2 rules, and draw that many cards.
For example: If you replace a Draw 2 with a new Draw 5, you would get to draw 3 more cards immediately (5 - 2 = 3 new cards).
Note: You never have to discard cards if the new Draw Rule is less than old one.