Priest was born in Maury County, Tennessee. He attended Central High School in Columbia, and afterward continued his education at State Teachers' College in Murfreesboro (now Middle Tennessee State University), and the former Peabody College in Nashville. He taught school in Culleoka, in his native Maury County, from 1920 until 1926, when he joined the editorial staff of the Nashville Tennessean.
In 1940 Priest was encouraged to run for the United States House of Representatives as an independent in Tennessee's 5th District, which was, then as now, based in Nashville. He won in an upset, defeating the incumbent one-term Democratic Congressman Jo Byrns, Jr. Upon swearing-in he immediately joined the Democratic caucus, and was reelected seven times. The district was renumbered the 6th District in 1943 and became the 5th once again in 1953. He served as the House majority whip between 1949 and 1953. Priest was one of three Democrats in the Tennessee House delegation who didn't sign the Southern Manifesto, the others being Joe Evins and Ross Bass.
At the time of his death, Priest was serving as the chairman of the House Commerce Committee and had already secured the Democratic nomination for a ninth term, which had essentially assured him of reelection since no Republican has been elected to the U.S. House of Representatives from Nashville since Reconstruction. Priest was interred at Woodlawn Cemetery in Nashville. J. Percy Priest Dam, a United States Army Corps of Engineers hydroelectric and flood control structure just east of Nashville on the Stones River (and easily visible from Interstate 40) is named in his honor, as is Percy Priest Lake (created by the dam), and also an elementary school