Tegart reached the final at Wimbledon in 1968, where she lost to Billie Jean King in two tight sets after defeating second-seeded Court in the quarterfinal and third-seeded Nancy Richey in the semifinal. She also reached the singles semifinals at Wimbledon in 1971 at the age of 33, losing to Court in three sets, and at the Australian Championships in 1968, losing to King in three sets. Her last appearance at a Grand Slam tournament was the 1977 Australian Open, where at the age of 40 she lost in the quarterfinals in straight sets to top-seeded and eventual champion Evonne Goolagong Cawley.