Starting with the upcoming season, players may now avoid a card, despite committing a foul, if the referee believes they made a deliberate attempt for the ball.
This will be a massive change, especially when it concerns the last man fouling a striker to prevent a goal-scoring opportunity. While historically that would almost always result in the defender being shown a straight red card, now they could escape with just a yellow if the referee determines that they made an honest attempt to win the ball.
While this one isn't necessarily new and was implemented last season, it is officially in writing now, with the objective to make offside-based decisions easier for referees and VAR.
The new law states that "a player who is clearly offside should not become onside on every occasion when an opponent moves and touches the ball." This means that it's no longer a guarantee that a player will be deemed onside if the ball touched an opponent before him.
It's there to clear up any doubt about how to correctly officiate the offside rule, with a lot of uncertainty surrounding it last season, with no one really quite on the same page.