Branden Dawson was drafted with the 56th pick in the 2015 draft. He appeared in 6 games for the Clippers, averaging 0.8 points, 0.7 rebounds, and 0.2 blocks in 4.8 minutes per game. Branden is only 23 years of age, and will be on waivers, meaning teams can bid to claim him on his previous contract, which is still non-guaranteed until the start of next season. Expect to see him in some team's training camp.
As for the Clippers, this brings their roster size back down to 14, which enables them to sign another player. Whether Doc will do so now, or will wait until some time in the regular season, is largely dependent on the futures of Paul Pierce and David Michineau. If Michineau is sent overseas or Pierce retires, another spot will open up, and the Clippers are likely to sign someone in the coming weeks. If not, Doc will probably want to keep a roster spot open during the season for flexibility in trades or in case a player he really likes is bought out.
The biggest hole for the Clippers is at small forward, and it would not surprise me to see news of Doc signing someone at that position shortly-- the Clippers had until November to cut Dawson, and waiving him now means they probably have something ready to go. If not, we will just have to wait to see what happens with Pierce and Michineau.
Good luck to Branden Dawson! Hopefully he is able to find a good home in the NBA and have a nice career.