A company that takes over a unionized workplace and tries to dodge its bargaining obligations by not hiring some of the previous employer’s workers no longer has to adhere to the labor deal that was previously in place.

The National Labor Relations Board’s Republican members on April 2 overturned a Clinton-era decision that said successor employers that discriminate in hiring to any degree to avoid bargaining duties can’t set their own initial terms of employment. Now companies are denied that right only if they say they’re going to keep all of a predecessor’s workers or if their unlawful hiring scheme...