African Party for the Independence of Cape Verde
After briefly living in Angola from 1972 to 1974, Veiga returned to Cape Verde in 1975, the year that it became independent, to join the African Party for the Independence of Guinea and Cape Verde (PAIGC). During his time in the PAIGC, Veiga served the Ministry of Public Administration from 1975 to 1980 as a judge. After leaving the African Party for the Independence of Cape Verde, he resumed his legal career and led the bar of Cape Verde from 1982 to 1986.