Sinha, has been actively involved in working for the backward villages of eastern Uttar Pradesh. His political career began in 1982 when he was elected the president of Banaras Hindu University(BHU) Students Union. He was elected to the Lok Sabha for the first time in 1996 and repeated the term in 1999.
From 1989 to 1996, Sinha remained a member of the BJP national council. He was elected to the Lower House for a third term in national politics when the BJP swept the Lok Sabha elections in 2014.
Political observers believe that appointment of a political leader as the Lt Governor indicates a great thrust in the days ahead to create conducive conditions to start the political process in Jammu and Kashmir.