In 1985-1990 Liabiedźka worked as deputy director of a boarding school in Ašmiany district. He was elected a deputy of the Supreme Council of the 12th and 13th convocations. During the 1994 presidential campaign he worked in Lukashenka's team, but soon moved to the opposition camp. In 1992-1999 he was President of the Belarusian Association of Young Politicians. He joined the United Civic Party and in 2000 was elected its deputy chairman. On 15 April 2000 he was elected chairman of the United Civic Party. He ran for MP at the House of Representatives in the 2008 elections.