Raised in Newton Mearns, Carlaw worked as a car salesman after education at The Glasgow Academy. Elected to the Scottish Parliament on the West of Scotland regional list in 2007 and 2011, he was elected as Deputy Leader of the Scottish Conservative Party in the 2011 deputy leadership election. He was subsequently made Scottish Conservative Spokesperson for Health and Sport. He was elected to the constituency of Eastwood in 2016, which had contested previously in 2003, 2007, and 2011, and following the election was made Shadow Cabinet Secretary for Europe and External Affairs and Shadow Cabinet Secretary for Culture and Tourism.