Tagelagi was first elected to the Niue Assembly at the 2008 Niuean general election. Following the 2014 Niuean general election he was appointed Minister of Infrastructure. He was re-elected at the 2017 Niuean general election, and subsequently served as Minister for the Environment, Natural Resources, Agriculture, Forestry and Fisheries. As Environment Minister he represented Niue at the 2019 United Nations Climate Change Conference, calling for rich nations to show greater ambition.