Born in Memphis, Texas, Combest earned his Bachelor of Business Administration from West Texas State University in 1969. His family had operated a farm in West Texas for four generations. He served as Director of the Agriculture Stablization and Conservation Service of the U.S. Department of Agriculture for part of 1971. He served as a legislative assistant to Senator John Tower from 1971-1978. After leaving Tower's office, Combest became a businessman.

In 1984, Democratic Congressman Kent Hance did not run for a fourth term, opting instead to run for the United States Senate. Combest won the Republican nomination, and was elected in November with 58f the vote amid Ronald Reagan's landslide reelection victory that year. Combest was only the third person to represent the 19th District since its creation in 1934. He was also the first Republican, even though the 19th had become increasingly friendly to Republicans over the years (a Democratic presidential candidate has not carried the district since 1964. He was reelected nine times with no substantive Democratic opposition, running unopposed in 1990, 1994 and with no major-party opposition in 2000 and 2002.

Combest served as chaired of the House Intelligence Committee in the 104th Congress (1995-1997) and Chairman of the House Agriculture Committee in the 106th and 107th Congresses (1999-2003). His voting record was solidly conservative, but his approach was not nearly as confrontational as other conservative Republicans. For instance, he and Democrat Charlie Stenholm (himself a farmer), the ranking member on the Agriculture Committee worked together very closely to shepherd the 2002 Farm Bill to passage.

After the deaths of his father and daughter, Combest announced his resignation on November 12, 2002--only a week after winning a 10th term. He said that he and his wife, Sharon, "realize how fragile life and health are. They certainly caused us to rearrange our priorities and we want to spend as much time together while we have our life and health." He resigned from the House on May 31, 2003. Fellow Republican Randy Neugebauer won the special election to replace Combest and was sworn into office on June 5, 2003.