At the 2012 U.S. Open Swimming Championships in Indianapolis, Conger took silver in the 200-meter backstroke with a time of 1:58.14. At the 2012 United States Olympic Trials, Conger missed the U.S. Team by finishing 8th in the 100-meter backstroke and 5th in the 200-meter backstroke with times of 54.63 and 1:58.97, respectively. At the 2012 Junior Pan Pacific Swimming Championships, Conger broke the national age-group record for the 17–18 age group in the 100-meter backstroke with a winning time of 54.07. He also took home two more golds in the 200-meter backstroke, 50-meter freestyle, and one bronze in the 100-meter freestyle. At the 2013 Summer Universiade in Kazan, Conger, competing as an incoming freshman, won gold in the 200-meter backstroke with a time of 1:55.47, and bronze as a member of the U.S. team in the 4x100-meter medley relay. Conger also competed in the 100-meter butterfly and finished 6th in the final. Conger accepted an athletic scholarship to attend the University of Texas at Austin, where he swims for coach Eddie Reese's Texas Longhorns men's swimming team. On February 25, 2015, Conger broke the American and US Open record in the 200-yard butterfly. Conger time trialed the event during the 2015 Big 12 Championships. At the 2015 NCAA Championships, Conger won the silver in the 100 and 200 yard butterfly behind teammate Joseph Schooling. He finished 7th in the 100 yard backstroke, with a time of 45.76. Conger helped the Texas Longhorns in the 400 yard medley relay, the 800 yard freestyle relay on Day 2, and the 400 yard freestyle relay on Day 3. At the 2015 U.S Nationals in San Antonio, Conger competed in the 100 and 200 meter butterfly, the 200 m backstroke, the 100 m freestyle, and the 200 meter freestyle. Conger finished second to Michael Phelps in both the 100 m and 200 m butterfly, recording times of 51.33 and 1:54.54 respectively. He narrowly missed his personal best in the 100 m freestyle, going 49.05 to miss it by.03. He finished second to Caeleb Dressel in that race. Conger qualified first after prelims in the 200 m freestyle, but withdrew to focus on the 200 butterfly. In the 200 m backstroke, Conger finished in 4th place with a time of 1:58.84.
2016 Summer Olympics
Conger represented the United States in the 2016 Olympics in Rio, having qualified in the U.S. Olympic Trials winning bronze in the 200 meter freestyle. At the Olympics, Conger swam in the heats of the 4 × 200 meter freestyle relay and secured qualification for the final with a fast last 50 meter split of 26.83. Although Conger posted the fastest split time of the American team in the heats, he was left off the team that swam the final. The team went on to win the final, also earning Conger a gold medal.
Gas station incident during 2016 Olympics
On the morning of August 14, Conger's teammate Ryan Lochte claimed that he, Conger, Gunnar Bentz, and Jimmy Feigen were robbed after four men forced them out of their taxi at gunpoint. The Brazilian authorities questioned this account, and after Lochte had flown home on August 16, Conger and Bentz were prevented from leaving the country and their passports were seized; this was done in order to have them testify as witnesses of the incident. Civil Police of Rio de Janeiro concluded that the athletes were not robbed, but instead had been involved in an incident at a gas station in Barra da Tijuca, west of the city. The investigation found that the swimmers had stopped at a gas station near Casa França, where they were involved in a confrontation with security guards regarding vandalism. Some or all of the swimmers had caused damages to objects in a bathroom while intoxicated. It was claimed that the swimmers had already paid in cash 100 reais and $20 in U.S. currency as compensation for objects from the bathroom which were damaged, such as a soap holder, a mirror, and a "Please Do Not Enter" sign. According to anonymous police sources, Conger and Bentz told the police that Lochte's robbery story was fabricated. The Associated Press reported that Conger and Bentz "refuted Lochte's claim that the group was held up by armed assailants". Conger stated the group was confronted by two armed security guards with guns, one "pointed at" Conger. After Conger returned to the United States, he apologized in a formal statement. He admitted the team had urinated on an alleyway wall, and that Lochte removed a poster from a wall. Fellow swimmer Gunnar Bentz stated the swimmers had returned to the taxi but were ordered out by two armed security men who pointed their guns at them, commanding them to sit on the pavement before an interpreter arrived. Both Conger and Bentz's statements maintained that Lochte ripped a poster and approached the guards, but denied witnessing any damage caused to the bathroom.
Post Rio
At the 2017 NCAA Championships, Conger helped lead the Longhorns to their third-straight team title. He broke the U.S. Open and American Records in the 200 fly individually, and was part of three championships relays for Texas.
