In 1957, at the age of seventeen, Moore was elected governor of the Baton Rouge-based Boys State government/citizenship program.

He was admitted to the bar in 1966 and the next year joined the Baton Rouge law firm Dale, Woen, Richardson, Taylor, and Mathews, first as an associate and then as a full member.

He succeeded John Richard Rarick of St. Francisville in West Feliciana Parish north of Baton Rouge.

...[2]Moore stressed in speeches that the longstanding American deficit is financed by foreign capital, whose owners consider the United States a good place in which to invest.

[2] Moore was the first Republican to run for the United States Senate with party organizational support since 1962, when Taylor W. O'Hearn of Shreveport unsuccessfully challenged Russell Long.

He was also the first candidate to declare for Long's seat after the veteran lawmaker announced his retirement effective in January 1987.

He had the immediate support of Republican colleague Bob Livingston of First District, who in 1987 launched an unsuccessful bid for governor of Louisiana.

Republican chairman George J. Despot of Shreveport pronounced Moore's as his party's "strongest possibility" to fill Long's seat.

[4] Also strongly for Moore was his friend Frank Spooner, the outgoing Republican national committeeman and an oil and natural gas producer in Monroe, who had lost the 1976 race for Louisiana's 5th congressional district to the Democrat Jerry Huckaby.

[5] In this campaign, Moore sounded more like a candidate for governor than for the U.S. Senate, having consistently claimed that Louisiana needed "a new image".

He specifically called for greater job opportunities, expanded port facilities and exports, more emphasis on tourism, and the designation of a research hospital in Louisiana.

[citation needed] After his House service, U.S. President Ronald Reagan named Moore commissioner of the Panama Canal Consultative Committee (1987–1989).

In April 1989, he became deputy secretary of the United States Department of Energy, having been sworn into that position by then Vice President Dan Quayle.

His involvement – as spokesman and fundraiser – made a huge difference for his alma mater, future generations of students and faculty, and for Louisiana.

On April 1, 2011, Moore was honored as the 2011 Alumnus of the Year as part of the LSU Alumni Association's Hall of Distinction.