Legislative efforts to rein in proxy advisory firms’ influence over executive pay and other corporate ballot items will continue into next Congress as regulators consider their own action.

Lawmakers in both chambers have introduced bills that would add regulatory oversight for proxy advisers, which institutional investors hire for recommendations on how to vote their shares in public companies. Legislative action is unlikely in the current session of Congress, which ends Jan. 3. But the bills’ sponsors—Rep. Sean Duffy (R-Wis.) and...