Final answer:
The Republican President who led Progressive reforms after succeeding William McKinley was Theodore Roosevelt. He was followed by William Howard Taft, who continued some reforms but lost Roosevelt's support, leading to the election of Woodrow Wilson.
Step-by-step explanation:
The Republican President who succeeded William McKinley and led the way for Progressive reforms at the federal level was Theodore Roosevelt. After President McKinley was assassinated in 1901, Roosevelt stepped into the role and ushered in an era of progressive national politics. He is known for taking on big business, supporting workers in disputes, and conserving federal lands. His progressive actions set a new precedent for presidential duties in the 20th century. Although he became President by chance, his influence on Progressivism and the executive role was significant. He confronted business trusts, preserved natural resources, and was followed by William Howard Taft, who continued some of these reforms but eventually lost the support of Roosevelt.