When Abrahams returned to Jamaica, he became involved in the tourism industry, overseeing increased efforts to advertise Jamaica and its culture as the youngest director of tourism yet. Abrahams was a member of the Jamaican Senate (1977) and a director of Air Jamaica. After being elected to the Jamaican Parliament in 1980, the Prime Minister of Jamaica, Edward Seaga, made him the first dedicated minister of tourism in a Jamaican cabinet. As minister, Abrahams led a revitalization of the nation's tourism industry. He was also a advocate for the 1983 United States invasion of Grenada. Abrahams left his post of minister in 1984, officially for "personal reasons", though the actual reason is unclear. He was a member of the Jamaica Labour Party until 1985 and served four years in parliament as an independent, not running for re-election in 1989.