Palmer served as President of the Alabama Policy Institute for 24 years. During his tenure, the Alabama Policy Institute became a full-spectrum public policy organization that engaged in virtually all policy issues that affected Alabamians. It is considered the premier conservative think-tank in Alabama.

Palmer also was a founding member of the board of directors of the State Policy Network, an umbrella organization for various state-based think-tanks. He served on the State Policy Network board for six years, the last two as chairman. Leading this broad coalition of policy thinkers gave Palmer exposure and knowledge of policy problems that confront all 50 states. When State Policy Network was founded in 1992, there were fewer than 20 state think-tanks in their network. Today, State Policy Network has 65 member organizations.

Palmer served on four different state commissions on behalf of three different Governors. He was appointed to the Welfare Reform Commission by Governor Fob James. He also served as an advisor to Governor James' Aerospace, Science and Technology Task Force. He was appointed to the Task Force to Strengthen Alabama Families by Governor Bob Riley, and the Alabama Commission on Improving State Government by Governor Robert Bentley.

In 2014, he was elected to the 114th Congress, having never served in office before. In Congress, Palmer is focused on paying down the national debt by cutting spending; regulatory reform by reducing the number and expense of federal regulations; lowering energy costs and spurring economic growth and job creation by accessing America's vast energy resources; and replacing Obamacare with a health care plan that puts people back in charge of their health care decisions and that will truly make health care affordable and available; and protecting life in all its forms. Palmer serves on the House Oversight and Accountability Committee, the House Energy and Commerce Committee, and the Subcommittees on Energy, Environment and Climate Change, and Oversight and Investigations. Palmer has also served as the Chairman of the House Republican Policy Committee since the 116th Congress. The Republican Policy Committee aims to unite Congressional Republicans on policy and help advise other members of leadership on policy decisions.

Palmer has been a member of the Rotary Club of Birmingham since 1993, and he is a Paul Harris Fellow. He holds an Honorary Doctorate from the University of Mobile. He and his wife Ann live in Hoover, Alabama where they attend Briarwood Presbyterian Church in Birmingham, Alabama. They have three children, Claire, Kathleen and Rob.