Beasley will have to earn more minutes just like he had all season, by being a better defender and not be a complete bone head when he tries to create offense for others when he is driving.

Once Beasley figures out how to be a positive contributor on both sides of the ball, Lance Thomas will only play for spot minutes, leaving Beasley to take the lions share of minutes off the bench.
Beasley showed that he can do well playing off the ball in that last Lakers game, and his surprisingly heady play at the end of the Boston game helped carry the win.

Once he figures out how to be a plus player on both sides of the ball and contribute consistently in that manner, he'll pick up a few more minutes.