Upon graduating from law school on 1930, Brady joined his father's firm, Brady, Dean and Hobbs. In July 1963, he was appointed an Associate Justice of the Mississippi Supreme Court to complete the unexpired term of Justice R. Olney Arrington, and would serve until his death. While there, in spite of his personal segregationist views, he ruled on 1965 a White-only park in Greenwood was to be integrated, and vacated one year later the conviction of a Black by an All-White grand jury.
Political activism
In an interview, Brady affirmed his passion for politics came on 1932, when he heard Paul B. Johnson Sr. and Martin Sennet Conner in Brookhaven. That year he attended his first Democratic National Convention in Chicago; followed by the DNC in Chicago in 1936, the 1948 event in Philadelphia, during which he was the Chairman of the Speakers Bureau for the Dixiecrats, and the 1960 one in Atlantic City. He served as a Democratic National Committeeman from 1960 to 1964, on the urging of Ross Barnett and State Executive Committee members who wanted an anti-Civil Rights delegate to the Convention, and who thereafter refused to sign any loyalty pledge, describing this obligation as "smack of totalitarianism". Brady rose to national prominence through his strident discourse against civil rights and integration. On October 28, 1954 while a Mississippi Circuit Court Judge he delivered an address entitled 'Black Monday' to the Sons of the American Revolution in Greenwood, Mississippi, which he later published in an eponymously-titled book. He later gave the copyrights to the Citizens' Council, earning them enough funds to operate. In 1965, Time magazine called Brady "the philosopher of Mississippi's racist white Citizens' Councils." He later affirmed he was offered three times since 1925 to join the Ku Klux Klan but always refused.
Political and racial views
Brady was a white supremacist: in Black Monday Brady opined on the sanctity of Southern white women and the bestiality of Blacks:
You can dress a chimpanzee, housebreak him, and teach him to use a knife and fork, but it will take countless generations of evolutionary development, if ever, before you can convince him that a caterpillar or a cockroach is not a delicacy. Likewise the social, political, economical, and religious preferences of the negro remain close to the caterpillar and the cockroach. This is not stated to ridicule or abuse the negro. There is nothing fundamentally wrong with the caterpillar or the cockroach. It is merely a matter of taste. A cockroach or caterpillar remains proper food for a chimpanzee.