"K" is Royal's given middle name, not an abbreviation. He received it in honor of his mother, Katy, who died when he was an infant. She died of cancer, but because of the stigma surrounding the disease at that time, Royal was led to believe until he was an adult that she had died giving birth to him.
Royal was most noted for his prowess as a defensive back, where his 18 career interceptions and his three interceptions in the 1947 game against Oklahoma A&M (now Oklahoma State) are still Sooner records.
Royal's part-time contributions as quarterback had a similar impact, despite the fact that he shared time with Jack Mitchell and Claude Arnold at the position. He threw a 43-yard pass against North Carolina in the 1949 Sugar Bowl. Royal holds the fourth-best winning percentage in school history (minimum 15 starts) with a 16–1 mark as a part-time quarterback starter. His 11–0 mark as a starter in 1949 ranks as one of the best seasons in school history.
Royal took over as head coach at the University of Texas (UT) on December 18, 1956. The team went from a 1–9 record, their worst record ever, in 1956 to a 6–4–1 mark and a berth in the Sugar Bowl in 1957. Within two years, Royal had the Longhorns in the Cotton Bowl as the number-four team in the country. In Royal's 20 years as head coach, Texas never had a losing season. Royal posted a 167–47–5 career record at Texas. His overall coaching record was 184–60–5. Some of his most memorable games were against the University of Arkansas Razorbacks, and fellow College Football Hall of Fame head coach Frank Broyles.
With Royal at the helm, Texas won the school's first three undisputed national championships (1963, 1969 and 1970), won or shared 11 Southwest Conference championships, and made 16 bowl appearances. His 1963 and 1969 teams finished the season undefeated and untied—something no Longhorn team would do again until 2005.
Royal's teams were known for being very run-oriented. The quote, "Three things can happen when you pass, and two of them are bad," is often attributed to Royal, but Royal himself attributed it to another run-first coach, Woody Hayes.
Royal's coaching tactics were the subject of criticism in Gary Shaw's exposé of college football recruiting and coaching practices, Meat on the Hoof, which was published in 1972, six years after Shaw left the Texas football program.
Beginning in 1962, Royal also served as Texas's athletic director. He retired from coaching in 1976 and remained director of athletics until 1980. He then served as special assistant to the university president on athletic programs.
During his tenure, Royal oversaw the integration of African-Americans into the UT athletics program. At that time, while UT began admitting black students in 1956 and opening the athletics program to them in 1963, there were no black student-athletes well into the late 1960s. In 2005, Royal retrospectively noted that "things they are a-changing. But they weren't changing that quickly around here at the time.". He offered a scholarship to Julius Whittier of San Antonio after the last recipient dropped out due to poor academic performance, and Whittier became the first black student-athlete to play for the Texas Longhorns football team. Whittier went on to graduate from the Lyndon B. Johnson School of Public Affairs in 1976 with a master's degree and works as a chief prosecutor with the Dallas District Attorney's Office.
Royal also coached Freddie Steinmark, who was a member of the 1969 Longhorns National Championship team and subsequently died from bone cancer. Steinmark has been the topic of several books and a 2015 movie, My All American where Royal was portrayed by Aaron Eckhart.
Royal was survived by his wife Edith (b. 1925), whom he married on July 26, 1944. They have a son, Sammy Mack, and two predeceased children, Marian Royal Kazen (1945–73) and David Wade Royal (1952–82), both of whom died in automobile-related accidents.