Two Trump administration appointees on the National Labor Relations Board said they’re open to reconsidering long-standing precedent limiting when workers can try to vote out a union.

The NLRB’s 1951 decision in Poole Foundry & Machine Co. says that when an employer and a union reach a settlement agreement that provides for bargaining on a labor contract, that union’s status as exclusive bargaining agent can’t be challenged until a reasonable amount of time has elapsed. The board uses a multifactor test to determine whether a reasonable time has passed.

Republican NLRB Members William Emanuel and Marvin Kaplan said in an...