A native of New Iberia in Iberia Parish, Landry is a veteran of the United States Army who served in the Vietnam War. After service with the New Iberia Police Department and employment by Shell Oil, he was admitted in 1977 to the state police academy in Baton Rouge, from which he subsequently graduated.
In the state police, Landry held nearly every major leadership position, including chief of staff, detective, commander of protective services, deputy superintendent of patrol and support, sergeant, road supervisor, director of investigative support, and director of the gaming enforcement division. In 2000, Republican Governor Murphy J. Foster, Jr., named Landry, then an Independent, as police superintendent.
Since retirement from the state police, Landry has been director of security for the New Orleans International Airport and the chief of police for Southern University and Baton Rouge Community College.
Landry and his wife, the former Sharon Broussard (born January 1951), have three children, Shauna, Terry, Jr. (born February 1981), and Tory. He is a fundraiser for the Immaculate Heart of Mary School in Lafayette but does not list a religious affiliation.
In 2007, Landry ran unsuccessfully as a "No Party" candidate for the District 44 seat in the Louisiana House. He finished in third place with 23 percent of the votes cast. Victory went to Democrat Rickey Hardy.
Landry rebounded in 2011 in District 96, for the seat held since 2005 by Democrat Juan LaFonta. Landry, as a Democrat, finished second in the nonpartisan blanket primary with 2,939 votes (31.8 percent). The top vote-getter was an Independent candidate, Eric Martin, who drew 3,760 votes (40.7 percent). Four other Democratic candidates held the balance of the vote. In the ensuing general election, another low turnout contest, Landry defeated Martin, 4,641 votes (56 percent) to 3,654 (44 percent).
Representative Landry, an African-American, is a member of the Louisiana Legislative Black Caucus, the Rural Caucus, and the Democratic Caucus. He has an unusually heavy committee schedule, including the vice-chairmanship of the Transportation, Highways, and Public Works Committee. He also sits as well on (1) Administration of Criminal Justice, (2) Agriculture, Forestry, Aquaculture, and Rural Development, (3) Homeland Security (vice-chair of House select committee and on the joint committee), (4) Joint Capital Outlay, (5) Military and Veterans Affairs, and (6) Atchafalaya Basin Program Oversight Committee.
Landry's legislative ratings have ranged from 31 to 67 percent from the Louisiana Association of Business and Industry. In 2012, he was rated 17 percent by the National Federation of Independent Business. In 2013 and 2014, the conservative Louisiana Family Forum scored him 60 and 40 percent, respectively. In 2013 and 2014, he was rated 100 and 83 percent, respectively, by Louisiana Right to Life. He ranks 100 percent from the Louisiana Association of Educators.
In 2014, Landry voted for the requirement that abortion providers have hospital admitting privileges near their clinics; only five House members opposed the measure. That same year, he voted to extend the time for implementation of the Common Core State Standards Initiative. He voted to forbid the transportation of dogs in open truck beds on interstate highways. He voted to repeal the anti-sodomy laws, but the measure failed, 27-67.
In 2013, Landry voted to reduce penalties for the possession of marijuana. He opposed lifetime concealed carry gun permits and the use of such permits in restaurants that serve alcoholic beverages. He also voted to make information on weapon permits part of the public record. He voted to increase judicial pay and to end the mandatory retirement age for judges. In 2012, he voted to prohibit the use of cell phones while driving. He opposed state tax incentives to recruit a National Basketball Association team to Louisiana; he opposed state income tax deductions for taxpayers contributing to scholarship funds. He co-sponsored parole eligibility for non-violent offenders. He opposed reducing the number of hours that polling locations remain open. Louisiana has traditionally had 14-hour polling days. He opposed the requirement for drug testing of welfare recipients.
On May 15, 2017, Landry opposed in the House Transportation Committee a bill submitted by the Republican Larry Bagley of DeSoto Parish, which would have ended most automobile inspections in the state. Landry questioned whether Bagley's legislation would be "sacrificing safety. I just fundamentally disagree with your bill." Louisiana hence remains one of thirteen states with motor vehicle inspection laws.