MIke Clevinger will not be disciplined by MLB in regards to the abuse charge against him, but he is not off the hook:

The league also said in its statement that Clevinger voluntarily agreed to submit to evaluations by the joint treatment boards under the CBA and to comply with the boards recommendations. 

Yardbarker.com

I had to look up the joint treatment boards:

A joint policy board, consisting of three experts in the field and two representatives each from the MLBPA and the Commissioner’s Office has been established. The board is responsible for developing a treatment plan.

Players may be required to submit to psychological evaluations, attend counseling sessions, comply with court orders (including child support orders), relocate from a home shared with his partner, limit his interactions with his partner, relinquish all weapons, and other reasonable directives designed to promote the safety of the player’s partner, children, or victims.

Players who fail to comply are subject to discipline from the Commissioner. All information is to be kept confidential.

MLB.com

So we won’t hear about what the board decides unless Clevinger talks about it. I suspect the White Sox front office is breathing a sigh of relief.