One of a large political family, he served from 1936 to 1952 as a Democratic member of the Louisiana House of Representatives from Madison Parish.

His father's family were descended from John Sevier, a veteran of the American Revolution, and pioneer and first governor of Tennessee.

One of Henry's cousins was Andrew L. Sevier, who served as a Louisiana State Senator with repeated reelection, from 1932 until his death in office in 1962.

He was wounded sixteen times in France, and received the Purple Heart and the Silver Star medals.

The couple had three children: Carolyn S. Yerger (1921–1997), who married Rufus Taft Yerger, Sr. (1914–1973); Roberta Sevier Gandy (1924–2006), who married Robert Wyly Gandy, Jr. (1915–1987), and Henry Clay Sevier, Jr.[2] (1925–2016), who became an attorney and a partner in his father's law firm for a time and served on the Board of Governors of the Louisiana State Bar Association.

There Sevier entered into practice with Jefferson B. Snyder of Tallulah, the political boss of the delta parishes in northeastern Louisiana.

Sevier was elected a few months after the assassination of Governor Huey Pierce Long, Jr. At the time, there was much voter sympathy for the pro-Long faction.