By 2012, Nuquay served as the chair of the Ways, Means and Finance Committee, as well as a member of the following committees: Judiciary, Agriculture, Forestry and Fisheries, Human and Civil Rights, and Joint Legislative Modernization.
[2] From October 2016 to 15 January 2018 Nuquay served as speaker of the House of Representatives of Liberia.
Boakai was defeated by Coalition for Democratic Change nominee George Weah.
In 2018, President Weah appointed Nuquay as Director General of the Liberia Civil Aviation Authority.
[5] The same year, Nuquay ran for the Liberian Senate under the PUP banner, winning the Margibi seat.